diff --git a/cmd/config/internal/commands/run-fns.go b/cmd/config/internal/commands/run-fns.go
index f31d2fe7f..523cf9015 100644
--- a/cmd/config/internal/commands/run-fns.go
+++ b/cmd/config/internal/commands/run-fns.go
@@ -11,6 +11,7 @@ import (
 	"github.com/spf13/cobra"
 	"sigs.k8s.io/kustomize/cmd/config/internal/generateddocs/commands"
 	"sigs.k8s.io/kustomize/kyaml/errors"
+	"sigs.k8s.io/kustomize/kyaml/kio/filters"
 	"sigs.k8s.io/kustomize/kyaml/runfn"
 	"sigs.k8s.io/kustomize/kyaml/yaml"
 )
@@ -55,8 +56,8 @@ func GetRunFnRunner(name string) *RunFnRunner {
 	r.Command.Flags().StringVar(
 		&r.NetworkName, "network-name", "bridge", "the docker network to run the container in")
 	r.Command.Flags().StringSliceVar(
-		&r.Volumes, "volume", []string{},
-		"the volumes to bind mount to the container.")
+		&r.Mounts, "mount", []string{},
+		"a list of storage options read from the filesystem")
 	return r
 }
 
@@ -78,7 +79,7 @@ type RunFnRunner struct {
 	RunFns             runfn.RunFns
 	Network            bool
 	NetworkName        string
-	Volumes            []string
+	Mounts             []string
 }
 
 func (r *RunFnRunner) runE(c *cobra.Command, args []string) error {
@@ -203,6 +204,14 @@ data: {}
 	return []*yaml.RNode{rc}, nil
 }
 
+func toStorageMounts(mounts []string) []filters.StorageMount {
+	var sms []filters.StorageMount
+	for _, mount := range mounts {
+		sms = append(sms, filters.StringToStorageMount(mount))
+	}
+	return sms
+}
+
 func (r *RunFnRunner) preRunE(c *cobra.Command, args []string) error {
 	if r.EnableStar != (r.StarPath != "") {
 		return errors.Errorf("must specify --star-path with --enable-star")
@@ -244,6 +253,9 @@ func (r *RunFnRunner) preRunE(c *cobra.Command, args []string) error {
 		path = args[0]
 	}
 
+	// parse mounts to set storageMounts
+	storageMounts := toStorageMounts(r.Mounts)
+
 	r.RunFns = runfn.RunFns{
 		FunctionPaths:  r.FnPaths,
 		GlobalScope:    r.GlobalScope,
@@ -254,7 +266,7 @@ func (r *RunFnRunner) preRunE(c *cobra.Command, args []string) error {
 		Network:        r.Network,
 		NetworkName:    r.NetworkName,
 		EnableStarlark: r.EnableStar,
-		Volumes:        r.Volumes,
+		StorageMounts:  storageMounts,
 	}
 
 	// don't consider args for the function
diff --git a/cmd/config/internal/commands/run_test.go b/cmd/config/internal/commands/run_test.go
index 887451035..a3e8f492d 100644
--- a/cmd/config/internal/commands/run_test.go
+++ b/cmd/config/internal/commands/run_test.go
@@ -27,7 +27,7 @@ func TestRunFnCommand_preRunE(t *testing.T) {
 		functionPaths []string
 		network       bool
 		networkName   string
-		volumes       []string
+		mount         []string
 	}{
 		{
 			name: "config map",
@@ -217,17 +217,14 @@ apiVersion: v1
 `,
 		},
 		{
-			name:    "volumes",
-			args:    []string{"run", "dir", "--volume", "vol1", "--volume", "vol2"},
-			path:    "dir",
-			volumes: []string{"vol1", "vol2"},
-		},
-		{
-			name: "custom kind with volumes",
+			name: "custom kind with storage mounts",
 			args: []string{
-				"run", "dir", "--volume", "vol", "--image", "foo:bar", "--", "Foo", "g=h", "i=j=k"},
-			path:    "dir",
-			volumes: []string{"vol"},
+				"run", "dir", "--mount", "type=bind;src=/mount/path;dst=/local/",
+				"--mount", "type=volume;src=myvol;dst=/local/",
+				"--mount", "type=tmpfs;dst=/local/",
+				"--image", "foo:bar", "--", "Foo", "g=h", "i=j=k"},
+			path:  "dir",
+			mount: []string{"type=bind;src=/mount/path;dst=/local/", "type=volume;src=myvol;dst=/local/", "type=tmpfs;dst=/local/"},
 			expected: `
 metadata:
   name: function-input
@@ -327,12 +324,7 @@ apiVersion: v1
 				t.FailNow()
 			}
 
-			// check if Volumes were set
-			if tt.volumes == nil {
-				// make Equal work against flag default
-				tt.volumes = []string{}
-			}
-			if !assert.Equal(t, tt.volumes, r.RunFns.Volumes) {
+			if !assert.Equal(t, toStorageMounts(tt.mount), r.RunFns.StorageMounts) {
 				t.FailNow()
 			}
 
diff --git a/kyaml/kio/filters/container.go b/kyaml/kio/filters/container.go
index 663774356..54dfdec57 100644
--- a/kyaml/kio/filters/container.go
+++ b/kyaml/kio/filters/container.go
@@ -134,11 +134,8 @@ type ContainerFilter struct {
 	// Network is the container network to use.
 	Network string `yaml:"network,omitempty"`
 
-	// Volumes are the directories to mount as container volumes.
-	Volumes []string `yaml:"volumes,omitempty"`
-
 	// StorageMounts is a list of storage options that the container will have mounted.
-	StorageMounts []StorageMount
+	StorageMounts []StorageMount `yaml:"mounts,omitempty"`
 
 	// Config is the API configuration for the container and passed through the
 	// API_CONFIG env var to the container.
@@ -159,25 +156,31 @@ func (c ContainerFilter) String() string {
 	return c.Image
 }
 
-// StorageMount represents a container's mounted storage option(s)
-type StorageMount struct {
-	// Type of mount e.g. bind mount, local volume, etc.
-	MountType string
-
-	// Source for the storage to be mounted.
-	// For named volumes, this is the name of the volume.
-	// For anonymous volumes, this field is omitted (empty string).
-	// For bind mounts, this is the path to the file or directory on the host.
-	Src string
-
-	// The path where the file or directory is mounted in the container.
-	DstPath string
-}
-
 func (s *StorageMount) String() string {
 	return fmt.Sprintf("type=%s,src=%s,dst=%s:ro", s.MountType, s.Src, s.DstPath)
 }
 
+func StringToStorageMount(s string) StorageMount {
+	m := make(map[string]string)
+	options := strings.Split(s, ";")
+	for _, option := range options {
+		keyVal := strings.Split(option, "=")
+		m[keyVal[0]] = keyVal[1]
+	}
+	var sm StorageMount
+	for key, value := range m {
+		switch {
+		case key == "type":
+			sm.MountType = value
+		case key == "src":
+			sm.Src = value
+		case key == "dst":
+			sm.DstPath = value
+		}
+	}
+	return sm
+}
+
 // functionsDirectoryName is keyword directory name for functions scoped 1 directory higher
 const functionsDirectoryName = "functions"
 
@@ -338,11 +341,6 @@ func (c *ContainerFilter) getArgs() []string {
 		args = append(args, "--mount", storageMount.String())
 	}
 
-	// export volumes to the container
-	for _, volume := range c.Volumes {
-		args = append(args, "--volume", volume)
-	}
-
 	// export the local environment vars to the container
 	for _, pair := range os.Environ() {
 		tokens := strings.Split(pair, "=")
diff --git a/kyaml/kio/filters/container_test.go b/kyaml/kio/filters/container_test.go
index 5d37ee55e..319a1a535 100644
--- a/kyaml/kio/filters/container_test.go
+++ b/kyaml/kio/filters/container_test.go
@@ -141,87 +141,6 @@ metadata:
 	assert.Equal(t, expected, cmd.Args)
 }
 
-func TestFilter_command_volume(t *testing.T) {
-	cfg, err := yaml.Parse(`apiVersion: apps/v1
-kind: Deployment
-metadata:
-  name: foo
-`)
-	if !assert.NoError(t, err) {
-		return
-	}
-	instance := &ContainerFilter{
-		Image:   "example.com:version",
-		Volumes: []string{"/host-src:/container-dest:ro"},
-		Config:  cfg,
-	}
-	cmd, err := instance.getCommand()
-	if !assert.NoError(t, err) {
-		return
-	}
-
-	expected := []string{
-		"docker", "run",
-		"--rm",
-		"-i", "-a", "STDIN", "-a", "STDOUT", "-a", "STDERR",
-		"--network", "none",
-		"--user", "nobody",
-		"--security-opt=no-new-privileges",
-		"--volume", "/host-src:/container-dest:ro",
-	}
-	for _, e := range os.Environ() {
-		// the process env
-		tokens := strings.Split(e, "=")
-		if tokens[0] == "" {
-			continue
-		}
-		expected = append(expected, "-e", tokens[0])
-	}
-	expected = append(expected, "example.com:version")
-	assert.Equal(t, expected, cmd.Args)
-}
-
-func TestFilter_command_volumes(t *testing.T) {
-	cfg, err := yaml.Parse(`apiVersion: apps/v1
-kind: Deployment
-metadata:
-  name: foo
-`)
-	if !assert.NoError(t, err) {
-		return
-	}
-	instance := &ContainerFilter{
-		Image:   "example.com:version",
-		Volumes: []string{"/host-src1:/container-dest1:ro", "/host-src2:/container-dest2:rw"},
-		Config:  cfg,
-	}
-	cmd, err := instance.getCommand()
-	if !assert.NoError(t, err) {
-		return
-	}
-
-	expected := []string{
-		"docker", "run",
-		"--rm",
-		"-i", "-a", "STDIN", "-a", "STDOUT", "-a", "STDERR",
-		"--network", "none",
-		"--user", "nobody",
-		"--security-opt=no-new-privileges",
-		"--volume", "/host-src1:/container-dest1:ro",
-		"--volume", "/host-src2:/container-dest2:rw",
-	}
-	for _, e := range os.Environ() {
-		// the process env
-		tokens := strings.Split(e, "=")
-		if tokens[0] == "" {
-			continue
-		}
-		expected = append(expected, "-e", tokens[0])
-	}
-	expected = append(expected, "example.com:version")
-	assert.Equal(t, expected, cmd.Args)
-}
-
 func TestFilter_Filter(t *testing.T) {
 	cfg, err := yaml.Parse(`apiVersion: apps/v1
 kind: Deployment
@@ -415,6 +334,68 @@ container:
     image: foo:v1.0.0`,
 		},
 
+		{
+			name: "storage mounts json style",
+			resource: `
+apiVersion: v1beta1
+kind: Example
+metadata:
+  annotations:
+    config.kubernetes.io/function: |-
+      container:
+        image: foo:v1.0.0
+        mounts: [ {type: bind, src: /mount/path, dst: /local/}, {src: myvol, dst: /local/, type: volume}, {dst: /local/, type: tmpfs} ]
+`,
+			expectedFn: `
+container:
+    image: foo:v1.0.0
+    mounts:
+      - type: bind
+        src: /mount/path
+        dst: /local/
+      - type: volume
+        src: myvol
+        dst: /local/
+      - type: tmpfs
+        dst: /local/
+`,
+		},
+
+		{
+			name: "storage mounts yaml style",
+			resource: `
+apiVersion: v1beta1
+kind: Example
+metadata:
+  annotations:
+    config.kubernetes.io/function: |-
+      container:
+        image: foo:v1.0.0
+        mounts:
+        - src: /mount/path
+          type: bind
+          dst: /local/
+        - dst: /local/
+          src: myvol
+          type: volume
+        - type: tmpfs
+          dst: /local/
+`,
+			expectedFn: `
+container:
+    image: foo:v1.0.0
+    mounts:
+      - type: bind
+        src: /mount/path
+        dst: /local/
+      - type: volume
+        src: myvol
+        dst: /local/
+      - type: tmpfs
+        dst: /local/
+`,
+		},
+
 		{
 			name: "network",
 			resource: `
@@ -436,70 +417,6 @@ container:
 `,
 		},
 
-		{
-			name: "volume",
-			resource: `
-apiVersion: v1beta1
-kind: Example
-metadata:
-  annotations:
-    config.kubernetes.io/function: |-
-      container:
-        image: foo:v1.0.0
-        volumes: ["/host-src:/container-dest:ro"]
-`,
-			expectedFn: `
-container:
-    image: foo:v1.0.0
-    volumes:
-      - /host-src:/container-dest:ro
-`,
-		},
-
-		{
-			name: "volumes as array",
-			resource: `
-apiVersion: v1beta1
-kind: Example
-metadata:
-  annotations:
-    config.kubernetes.io/function: |-
-      container:
-        image: foo:v1.0.0
-        volumes: ["/host-src1:/container-dest1:ro", "/host-src2:/container-dest2:rw"]
-`,
-			expectedFn: `
-container:
-    image: foo:v1.0.0
-    volumes:
-      - /host-src1:/container-dest1:ro
-      - /host-src2:/container-dest2:rw
-`,
-		},
-
-		{
-			name: "volumes as list",
-			resource: `
-apiVersion: v1beta1
-kind: Example
-metadata:
-  annotations:
-    config.kubernetes.io/function: |-
-      container:
-        image: foo:v1.0.0
-        volumes:
-        - "/host-src1:/container-dest1:ro"
-        - "/host-src2:/container-dest2:rw"
-`,
-			expectedFn: `
-container:
-    image: foo:v1.0.0
-    volumes:
-      - /host-src1:/container-dest1:ro
-      - /host-src2:/container-dest2:rw
-`,
-		},
-
 		{
 			name: "path",
 			resource: `
@@ -661,76 +578,6 @@ metadata:
 	}
 }
 
-func Test_GetContainerVolumeRequired(t *testing.T) {
-	tests := []struct {
-		input   string
-		volumes []string
-	}{
-		{
-			input: `apiVersion: v1
-kind: Foo
-metadata:
-  name: foo
-  configFn:
-    container:
-      image: gcr.io/kustomize-functions/example-tshirt:v0.1.0
-      volumes: [ /host-src:/container-dest:ro ]
-`,
-			volumes: []string{"/host-src:/container-dest:ro"},
-		},
-		{
-
-			input: `apiVersion: v1
-kind: Foo
-metadata:
-  name: foo
-  configFn:
-    container:
-      image: gcr.io/kustomize-functions/example-tshirt:v0.1.0
-`,
-			volumes: []string(nil),
-		},
-		{
-			input: `apiVersion: v1
-kind: Foo
-metadata:
-  name: foo
-  annotations:
-    config.kubernetes.io/function: |
-      container:
-        image: gcr.io/kustomize-functions/example-tshirt:v0.1.0
-        volumes: [ "/host-src1:/container-dest1:ro", "/host-src2:/container-dest2:rw" ]
-`,
-			volumes: []string{"/host-src1:/container-dest1:ro", "/host-src2:/container-dest2:rw"},
-		},
-		{
-			input: `apiVersion: v1
-kind: Foo
-metadata:
-  name: foo
-  annotations:
-    config.kubernetes.io/function: |
-      container:
-        image: gcr.io/kustomize-functions/example-tshirt:v0.1.0
-        volumes:
-          - /host-src1:/container-dest1:ro
-          - /host-src2:/container-dest2:rw
-`,
-			volumes: []string{"/host-src1:/container-dest1:ro", "/host-src2:/container-dest2:rw"},
-		},
-	}
-
-	for _, tc := range tests {
-		cfg, err := yaml.Parse(tc.input)
-		if !assert.NoError(t, err) {
-			return
-		}
-
-		fn := GetFunctionSpec(cfg)
-		assert.Equal(t, tc.volumes, fn.Container.Volumes)
-	}
-}
-
 func TestFilter_Filter_defaultNaming(t *testing.T) {
 	cfg, err := yaml.Parse(`apiVersion: apps/v1
 kind: Deployment
diff --git a/kyaml/kio/filters/functiontypes.go b/kyaml/kio/filters/functiontypes.go
index 4096cd952..db5a8adb3 100644
--- a/kyaml/kio/filters/functiontypes.go
+++ b/kyaml/kio/filters/functiontypes.go
@@ -29,8 +29,8 @@ type FunctionSpec struct {
 	// Starlark is the spec for running a function as a starlark script
 	Starlark StarlarkSpec `json:"starlark,omitempty" yaml:"starlark,omitempty"`
 
-	// Volumes are the directories to mount as container volumes
-	Volumes []string `json:"volumes,omitempty" yaml:"volumes,omitempty"`
+	// Mounts are the storage or directories to mount into the container
+	StorageMounts []StorageMount `json:"mounts,omitempty" yaml:"mounts,omitempty"`
 }
 
 // ContainerSpec defines a spec for running a function as a container
@@ -41,8 +41,8 @@ type ContainerSpec struct {
 	// Network defines network specific configuration
 	Network ContainerNetwork `json:"network,omitempty" yaml:"network,omitempty"`
 
-	// Volumes are the directories to mount as container volumes
-	Volumes []string `json:"volumes,omitempty" yaml:"volumes,omitempty"`
+	// Mounts are the storage or directories to mount into the container
+	StorageMounts []StorageMount `json:"mounts,omitempty" yaml:"mounts,omitempty"`
 }
 
 // ContainerNetwork
@@ -59,6 +59,21 @@ type StarlarkSpec struct {
 	Path string `json:"path,omitempty" yaml:"path,omitempty"`
 }
 
+// StorageMount represents a container's mounted storage option(s)
+type StorageMount struct {
+	// Type of mount e.g. bind mount, local volume, etc.
+	MountType string `json:"type,omitempty" yaml:"type,omitempty"`
+
+	// Source for the storage to be mounted.
+	// For named volumes, this is the name of the volume.
+	// For anonymous volumes, this field is omitted (empty string).
+	// For bind mounts, this is the path to the file or directory on the host.
+	Src string `json:"src,omitempty" yaml:"src,omitempty"`
+
+	// The path where the file or directory is mounted in the container.
+	DstPath string `json:"dst,omitempty" yaml:"dst,omitempty"`
+}
+
 // GetFunctionSpec returns the FunctionSpec for a resource.  Returns
 // nil if the resource does not have a FunctionSpec.
 //
@@ -74,7 +89,7 @@ func GetFunctionSpec(n *yaml.RNode) *FunctionSpec {
 	path := meta.Annotations[kioutil.PathAnnotation]
 	if fn := getFunctionSpecFromAnnotation(n, meta); fn != nil {
 		fn.Network = ""
-		fn.Volumes = []string{}
+		fn.StorageMounts = []StorageMount{}
 		fn.Path = path
 		return fn
 	}
diff --git a/kyaml/runfn/runfn.go b/kyaml/runfn/runfn.go
index 23ccd00f6..19d348486 100644
--- a/kyaml/runfn/runfn.go
+++ b/kyaml/runfn/runfn.go
@@ -51,10 +51,6 @@ type RunFns struct {
 	// NetworkName is the name of the docker network to use for the container
 	NetworkName string
 
-	// Volumes Volumes allows directories to be specified outside the configuration
-	// directory.
-	Volumes []string
-
 	// Output can be set to write the result to Output rather than back to the directory
 	Output io.Writer
 
@@ -137,13 +133,6 @@ func (r RunFns) getFilters(nodes []*yaml.RNode) ([]kio.Filter, error) {
 	}
 	fltrs = append(fltrs, f...)
 
-	// directories from volumes specified on the struct
-	f, err = r.getDirectoriesFromVolumes()
-	if err != nil {
-		return nil, err
-	}
-	fltrs = append(fltrs, f...)
-
 	// explicit fns specified on the struct
 	f, err = r.getFunctionsFromFunctions()
 	if err != nil {
@@ -207,24 +196,6 @@ func (r RunFns) getFunctionsFromFunctionPaths() ([]kio.Filter, error) {
 	return r.getFunctionFilters(true, buff.Nodes...)
 }
 
-// getDirectoriesFromVolumes returns the set of directories read from r.Volumes
-// as a slice of Filters
-func (r RunFns) getDirectoriesFromVolumes() ([]kio.Filter, error) {
-	buff := &kio.PackageBuffer{}
-	for i := range r.Volumes {
-		err := kio.Pipeline{
-			Inputs: []kio.Reader{
-				kio.LocalPackageReader{PackagePath: r.Volumes[i]},
-			},
-			Outputs: []kio.Writer{buff},
-		}.Execute()
-		if err != nil {
-			return nil, err
-		}
-	}
-	return r.getFunctionFilters(true, buff.Nodes...)
-}
-
 // getFunctionsFromFunctions returns the set of explicitly provided functions as
 // Filters
 func (r RunFns) getFunctionsFromFunctions() ([]kio.Filter, error) {
diff --git a/kyaml/runfn/runfn_test.go b/kyaml/runfn/runfn_test.go
index b3018129f..236f5610c 100644
--- a/kyaml/runfn/runfn_test.go
+++ b/kyaml/runfn/runfn_test.go
@@ -141,13 +141,13 @@ func TestRunFns_Execute__initDefault(t *testing.T) {
 			},
 		},
 		{
-			name:     "explicit directories in volumes",
-			instance: RunFns{Volumes: []string{"vol"}},
+			name:     "explicit directories in mounts",
+			instance: RunFns{StorageMounts: []filters.StorageMount{{MountType: "volume", Src: "myvol", DstPath: "/local/"}}},
 			expected: RunFns{
 				Output:               os.Stdout,
 				Input:                os.Stdin,
 				NoFunctionsFromInput: getFalse(),
-				Volumes:              []string{"vol"},
+				StorageMounts:        []filters.StorageMount{{MountType: "volume", Src: "myvol", DstPath: "/local/"}},
 			},
 		},
 	}