diff --git a/package.json b/package.json
index e3fea28ceb..e2e23f5b8e 100644
--- a/package.json
+++ b/package.json
@@ -106,7 +106,7 @@
     "jsdoc-fresh": "^1.0.1",
     "linkinator": "^1.5.0",
     "mocha": "^6.0.0",
-    "nock": "^11.0.0",
+    "nock": "~11.0.0",
     "node-fetch": "^2.2.0",
     "normalize-newline": "^3.0.0",
     "nyc": "^14.0.0",
diff --git a/src/file.ts b/src/file.ts
index 3de579d226..7067fb48c5 100644
--- a/src/file.ts
+++ b/src/file.ts
@@ -291,6 +291,7 @@ export interface FileOptions {
   generation?: number | string;
   kmsKeyName?: string;
   userProject?: string;
+  keepLeadingSlashes?: boolean;
 }
 
 export interface CopyOptions {
@@ -497,7 +498,9 @@ class File extends ServiceObject<File> {
    * const file = myBucket.file('my-file');
    */
   constructor(bucket: Bucket, name: string, options: FileOptions = {}) {
-    name = name.replace(/^\/+/, '');
+    if (options.keepLeadingSlashes !== true) {
+      name = name.replace(/^\/+/, '');
+    }
 
     const requestQueryObject: {generation?: number; userProject?: string} = {};
 
diff --git a/test/file.ts b/test/file.ts
index fb6535e5b2..c6f2e02d8c 100644
--- a/test/file.ts
+++ b/test/file.ts
@@ -244,6 +244,17 @@ describe('File', () => {
       assert.strictEqual(file.name, 'name');
     });
 
+    it('should strip two leading slashes', () => {
+      const file = new File(BUCKET, '//name');
+      assert.strictEqual(file.name, 'name');
+    });
+
+    it('should keep leading slashes when specified in options', () => {
+      const keepLeadingSlashes = true;
+      const file = new File(BUCKET, '/name', {keepLeadingSlashes});
+      assert.strictEqual(file.name, '/name');
+    })
+
     it('should assign KMS key name', () => {
       const kmsKeyName = 'kms-key-name';
       const file = new File(BUCKET, '/name', {kmsKeyName});