diff --git a/runtime/v1/linux/proc/deleted_state.go b/runtime/v1/linux/proc/deleted_state.go
index ab89c3ecb..fe9d7bf55 100644
--- a/runtime/v1/linux/proc/deleted_state.go
+++ b/runtime/v1/linux/proc/deleted_state.go
@@ -22,6 +22,7 @@ import (
 	"context"
 
 	"github.com/containerd/console"
+	"github.com/containerd/containerd/errdefs"
 	"github.com/containerd/containerd/runtime/proc"
 	google_protobuf "github.com/gogo/protobuf/types"
 	"github.com/pkg/errors"
@@ -55,11 +56,11 @@ func (s *deletedState) Start(ctx context.Context) error {
 }
 
 func (s *deletedState) Delete(ctx context.Context) error {
-	return errors.Errorf("cannot delete a deleted process")
+	return errors.Wrap(errdefs.ErrNotFound, "cannot delete a deleted process")
 }
 
 func (s *deletedState) Kill(ctx context.Context, sig uint32, all bool) error {
-	return errors.Errorf("cannot kill a deleted process")
+	return errors.Wrap(errdefs.ErrNotFound, "cannot kill a deleted process")
 }
 
 func (s *deletedState) SetExited(status int) {
diff --git a/runtime/v1/linux/task.go b/runtime/v1/linux/task.go
index 38da35c08..e13255e95 100644
--- a/runtime/v1/linux/task.go
+++ b/runtime/v1/linux/task.go
@@ -87,7 +87,7 @@ func (t *Task) Namespace() string {
 // Delete the task and return the exit status
 func (t *Task) Delete(ctx context.Context) (*runtime.Exit, error) {
 	rsp, err := t.shim.Delete(ctx, empty)
-	if err != nil {
+	if err != nil && !errdefs.IsNotFound(err) {
 		return nil, errdefs.FromGRPC(err)
 	}
 	t.tasks.Delete(ctx, t.id)
diff --git a/runtime/v2/shim.go b/runtime/v2/shim.go
index 65022390e..a32843b8b 100644
--- a/runtime/v2/shim.go
+++ b/runtime/v2/shim.go
@@ -152,7 +152,7 @@ func (s *shim) Delete(ctx context.Context) (*runtime.Exit, error) {
 	response, err := s.task.Delete(ctx, &task.DeleteRequest{
 		ID: s.ID(),
 	})
-	if err != nil {
+	if err != nil && errdefs.IsNotFound(err) {
 		return nil, errdefs.FromGRPC(err)
 	}
 	if err := s.waitShutdown(ctx); err != nil {