diff --git a/libcontainer/integration/template_test.go b/libcontainer/integration/template_test.go
index c9ebff7e0..039cd7375 100644
--- a/libcontainer/integration/template_test.go
+++ b/libcontainer/integration/template_test.go
@@ -2,6 +2,7 @@ package integration
 
 import (
 	"strconv"
+	"strings"
 	"testing"
 	"time"
 
@@ -215,7 +216,7 @@ func newTemplateConfig(t *testing.T, p *tParam) *configs.Config {
 
 	if p.systemd {
 		id := strconv.FormatInt(-int64(time.Now().Nanosecond()), 36)
-		config.Cgroups.Name = t.Name() + id
+		config.Cgroups.Name = strings.ReplaceAll(t.Name(), "/", "_") + id
 		// do not change Parent (see newContainer)
 		config.Cgroups.Parent = "system.slice"
 		config.Cgroups.ScopePrefix = "runc-test"
diff --git a/libcontainer/integration/utils_test.go b/libcontainer/integration/utils_test.go
index 0ffbf179b..b4fa6cf65 100644
--- a/libcontainer/integration/utils_test.go
+++ b/libcontainer/integration/utils_test.go
@@ -151,7 +151,7 @@ func copyBusybox(dest string) error {
 }
 
 func newContainer(t *testing.T, config *configs.Config) (libcontainer.Container, error) {
-	name := t.Name() + strconv.FormatInt(int64(time.Now().Nanosecond()), 35)
+	name := strings.ReplaceAll(t.Name(), "/", "_") + strconv.FormatInt(-int64(time.Now().Nanosecond()), 35)
 	root, err := newTestRoot()
 	if err != nil {
 		return nil, err