diff --git a/oci/spec_opts.go b/oci/spec_opts.go
index 55ccaf09a..050b445b8 100644
--- a/oci/spec_opts.go
+++ b/oci/spec_opts.go
@@ -961,6 +961,11 @@ func WithCapabilities(caps []string) SpecOpts {
 		s.Process.Capabilities.Bounding = caps
 		s.Process.Capabilities.Effective = caps
 		s.Process.Capabilities.Permitted = caps
+		if len(caps) == 0 {
+			s.Process.Capabilities.Inheritable = nil
+		} else if len(s.Process.Capabilities.Inheritable) > 0 {
+			filterCaps(&s.Process.Capabilities.Inheritable, caps)
+		}
 
 		return nil
 	}
@@ -986,6 +991,16 @@ func removeCap(caps *[]string, s string) {
 	*caps = newcaps
 }
 
+func filterCaps(caps *[]string, filters []string) {
+	var newcaps []string
+	for _, c := range *caps {
+		if capsContain(filters, c) {
+			newcaps = append(newcaps, c)
+		}
+	}
+	*caps = newcaps
+}
+
 // WithAddedCapabilities adds the provided capabilities
 func WithAddedCapabilities(caps []string) SpecOpts {
 	return func(_ context.Context, _ Client, _ *containers.Container, s *Spec) error {
@@ -1014,6 +1029,7 @@ func WithDroppedCapabilities(caps []string) SpecOpts {
 				&s.Process.Capabilities.Bounding,
 				&s.Process.Capabilities.Effective,
 				&s.Process.Capabilities.Permitted,
+				&s.Process.Capabilities.Inheritable,
 			} {
 				removeCap(cl, c)
 			}
diff --git a/oci/spec_opts_linux_test.go b/oci/spec_opts_linux_test.go
index b340c72e6..6e2bfc848 100644
--- a/oci/spec_opts_linux_test.go
+++ b/oci/spec_opts_linux_test.go
@@ -24,6 +24,7 @@ import (
 	"testing"
 
 	"github.com/containerd/containerd/containers"
+	"github.com/containerd/containerd/pkg/cap"
 	"github.com/containerd/containerd/pkg/testutil"
 	"github.com/containerd/continuity/fs/fstest"
 	specs "github.com/opencontainers/runtime-spec/specs-go"
@@ -216,6 +217,91 @@ sys:x:3:root,bin,adm
 	}
 }
 
+// withAllKnownCaps sets all known capabilities.
+// This function differs from the exported function
+// by also setting inheritable capabilities.
+func withAllKnownCaps(s *specs.Spec) error {
+	caps := cap.Known()
+	if err := WithCapabilities(caps)(context.Background(), nil, nil, s); err != nil {
+		return err
+	}
+	s.Process.Capabilities.Inheritable = caps
+	return nil
+}
+
+func TestSetCaps(t *testing.T) {
+	t.Parallel()
+
+	var s specs.Spec
+
+	// Add base set of capabilities
+	if err := WithCapabilities([]string{"CAP_CHOWN"})(context.Background(), nil, nil, &s); err != nil {
+		t.Fatal(err)
+	}
+	for i, cl := range [][]string{
+		s.Process.Capabilities.Bounding,
+		s.Process.Capabilities.Effective,
+		s.Process.Capabilities.Permitted,
+	} {
+		if !capsContain(cl, "CAP_CHOWN") {
+			t.Errorf("cap list %d does not contain added cap", i)
+		}
+		if len(cl) != 1 {
+			t.Errorf("cap list %d does not have only 1 cap", i)
+		}
+	}
+	if len(s.Process.Capabilities.Inheritable) != 0 {
+		t.Errorf("inheritable cap list is not empty")
+	}
+
+	// Add all caps then overwrite with single cap
+	if err := withAllKnownCaps(&s); err != nil {
+		t.Fatal(err)
+	}
+	if err := WithCapabilities([]string{"CAP_CHOWN"})(context.Background(), nil, nil, &s); err != nil {
+		t.Fatal(err)
+	}
+	for i, cl := range [][]string{
+		s.Process.Capabilities.Bounding,
+		s.Process.Capabilities.Effective,
+		s.Process.Capabilities.Permitted,
+		s.Process.Capabilities.Inheritable,
+	} {
+		if !capsContain(cl, "CAP_CHOWN") {
+			t.Errorf("cap list %d does not contain added cap", i)
+		}
+		if len(cl) != 1 {
+			t.Errorf("cap list %d does not have only 1 cap", i)
+		}
+	}
+
+	// Add all caps, drop single cap, then overwrite with single cap
+	if err := withAllKnownCaps(&s); err != nil {
+		t.Fatal(err)
+	}
+	if err := WithDroppedCapabilities([]string{"CAP_CHOWN"})(context.Background(), nil, nil, &s); err != nil {
+		t.Fatal(err)
+	}
+	if err := WithCapabilities([]string{"CAP_CHOWN"})(context.Background(), nil, nil, &s); err != nil {
+		t.Fatal(err)
+	}
+	for i, cl := range [][]string{
+		s.Process.Capabilities.Bounding,
+		s.Process.Capabilities.Effective,
+		s.Process.Capabilities.Permitted,
+	} {
+		if !capsContain(cl, "CAP_CHOWN") {
+			t.Errorf("cap list %d does not contain added cap", i)
+		}
+		if len(cl) != 1 {
+			t.Errorf("cap list %d does not have only 1 cap", i)
+		}
+	}
+	if len(s.Process.Capabilities.Inheritable) != 0 {
+		t.Errorf("inheritable cap list is not empty")
+	}
+}
+
 func TestAddCaps(t *testing.T) {
 	t.Parallel()
 
@@ -233,6 +319,9 @@ func TestAddCaps(t *testing.T) {
 			t.Errorf("cap list %d does not contain added cap", i)
 		}
 	}
+	if len(s.Process.Capabilities.Inheritable) != 0 {
+		t.Errorf("inheritable cap list is not empty")
+	}
 }
 
 func TestDropCaps(t *testing.T) {
@@ -240,7 +329,7 @@ func TestDropCaps(t *testing.T) {
 
 	var s specs.Spec
 
-	if err := WithAllKnownCapabilities(context.Background(), nil, nil, &s); err != nil {
+	if err := withAllKnownCaps(&s); err != nil {
 		t.Fatal(err)
 	}
 	if err := WithDroppedCapabilities([]string{"CAP_CHOWN"})(context.Background(), nil, nil, &s); err != nil {
@@ -251,6 +340,7 @@ func TestDropCaps(t *testing.T) {
 		s.Process.Capabilities.Bounding,
 		s.Process.Capabilities.Effective,
 		s.Process.Capabilities.Permitted,
+		s.Process.Capabilities.Inheritable,
 	} {
 		if capsContain(cl, "CAP_CHOWN") {
 			t.Errorf("cap list %d contains dropped cap", i)
@@ -258,7 +348,7 @@ func TestDropCaps(t *testing.T) {
 	}
 
 	// Add all capabilities back and drop a different cap.
-	if err := WithAllKnownCapabilities(context.Background(), nil, nil, &s); err != nil {
+	if err := withAllKnownCaps(&s); err != nil {
 		t.Fatal(err)
 	}
 	if err := WithDroppedCapabilities([]string{"CAP_FOWNER"})(context.Background(), nil, nil, &s); err != nil {
@@ -269,6 +359,7 @@ func TestDropCaps(t *testing.T) {
 		s.Process.Capabilities.Bounding,
 		s.Process.Capabilities.Effective,
 		s.Process.Capabilities.Permitted,
+		s.Process.Capabilities.Inheritable,
 	} {
 		if capsContain(cl, "CAP_FOWNER") {
 			t.Errorf("cap list %d contains dropped cap", i)
@@ -289,6 +380,25 @@ func TestDropCaps(t *testing.T) {
 		s.Process.Capabilities.Bounding,
 		s.Process.Capabilities.Effective,
 		s.Process.Capabilities.Permitted,
+		s.Process.Capabilities.Inheritable,
+	} {
+		if len(cl) != 0 {
+			t.Errorf("cap list %d is not empty", i)
+		}
+	}
+
+	// Add all capabilities back and drop all
+	if err := withAllKnownCaps(&s); err != nil {
+		t.Fatal(err)
+	}
+	if err := WithCapabilities(nil)(context.Background(), nil, nil, &s); err != nil {
+		t.Fatal(err)
+	}
+	for i, cl := range [][]string{
+		s.Process.Capabilities.Bounding,
+		s.Process.Capabilities.Effective,
+		s.Process.Capabilities.Permitted,
+		s.Process.Capabilities.Inheritable,
 	} {
 		if len(cl) != 0 {
 			t.Errorf("cap list %d is not empty", i)