diff --git a/memmap.go b/memmap.go
index 943bad0b..b8e19551 100644
--- a/memmap.go
+++ b/memmap.go
@@ -270,7 +270,7 @@ func (m *MemMapFs) RemoveAll(path string) error {
 	defer m.mu.RUnlock()
 
 	for p := range m.getData() {
-		if strings.HasPrefix(p, path) {
+		if strings.HasPrefix(p, path+FilePathSeparator) {
 			m.mu.RUnlock()
 			m.mu.Lock()
 			delete(m.getData(), p)
@@ -305,6 +305,18 @@ func (m *MemMapFs) Rename(oldname, newname string) error {
 	} else {
 		return &os.PathError{Op: "rename", Path: oldname, Err: ErrFileNotFound}
 	}
+
+	for p, fileData := range m.getData() {
+		if strings.HasPrefix(p, oldname+FilePathSeparator) {
+			m.mu.RUnlock()
+			m.mu.Lock()
+			delete(m.getData(), p)
+			p := strings.Replace(p, oldname, newname, 1)
+			m.getData()[p] = fileData
+			m.mu.Unlock()
+			m.mu.RLock()
+		}
+	}
 	return nil
 }
 
diff --git a/memmap_test.go b/memmap_test.go
index 47414ab1..05f0baf9 100644
--- a/memmap_test.go
+++ b/memmap_test.go
@@ -449,3 +449,47 @@ func TestMemFsUnexpectedEOF(t *testing.T) {
 		t.Fatal("Expected ErrUnexpectedEOF")
 	}
 }
+
+func TestMemFsRenameDir(t *testing.T) {
+	const srcPath = "/src"
+	const dstPath = "/dst"
+	const subDir = "dir"
+
+	fs := NewMemMapFs()
+
+	err := fs.MkdirAll(srcPath+FilePathSeparator+subDir, 0777)
+	if err != nil {
+		t.Errorf("MkDirAll failed: %s", err)
+		return
+	}
+
+	err = fs.Rename(srcPath, dstPath)
+	if err != nil {
+		t.Errorf("Rename failed: %s", err)
+		return
+	}
+
+	_, err = fs.Stat(srcPath + FilePathSeparator + subDir)
+	if err == nil {
+		t.Errorf("SubDir still exists in the source dir")
+		return
+	}
+
+	_, err = fs.Stat(dstPath + FilePathSeparator + subDir)
+	if err != nil {
+		t.Errorf("SubDir stat in the destination dir: %s", err)
+		return
+	}
+
+	err = fs.Mkdir(srcPath, 0777)
+	if err != nil {
+		t.Errorf("Cannot recreate the source dir: %s", err)
+		return
+	}
+
+	err = fs.Mkdir(srcPath+FilePathSeparator+subDir, 0777)
+	if err != nil {
+		t.Errorf("Cannot recreate the subdir in the source dir: %s", err)
+		return
+	}
+}