diff --git a/src/vs/editor/contrib/find/common/replacePattern.ts b/src/vs/editor/contrib/find/common/replacePattern.ts
index 7e15cdf97dacdb1555dd194f8be54cd28930d5d6..d721b7c03e0fab5073f303ab959b2fdba760fe2b 100644
--- a/src/vs/editor/contrib/find/common/replacePattern.ts
+++ b/src/vs/editor/contrib/find/common/replacePattern.ts
@@ -67,7 +67,9 @@ export class ReplacePattern {
 		let remainder = '';
 		while (matchIndex > 0) {
 			if (matchIndex < matches.length) {
-				return matches[matchIndex] + remainder;
+				// A match can be undefined
+				let match = (matches[matchIndex] || '');
+				return match + remainder;
 			}
 			remainder = String(matchIndex % 10) + remainder;
 			matchIndex = Math.floor(matchIndex / 10);
diff --git a/src/vs/editor/contrib/find/test/common/findModel.test.ts b/src/vs/editor/contrib/find/test/common/findModel.test.ts
index 73b2b1d6e15bd5d52540122ef760a3fa5db9df5b..5fbf02df835ea5b4a5a249c13df78131cf3febb9 100644
--- a/src/vs/editor/contrib/find/test/common/findModel.test.ts
+++ b/src/vs/editor/contrib/find/test/common/findModel.test.ts
@@ -2002,4 +2002,35 @@ suite('FindModel', () => {
 		findModel.dispose();
 		findState.dispose();
 	});
+
+	findTest('issue #19740 Find and replace capture group/backreference inserts `undefined` instead of empty string', (editor, cursor) => {
+		let findState = new FindReplaceState();
+		findState.change({ searchString: 'hello(z)?', replaceString: 'hi$1', isRegex: true, matchCase: true }, false);
+		let findModel = new FindModelBoundToEditorModel(editor, findState);
+
+		assertFindState(
+			editor,
+			[1, 1, 1, 1],
+			null,
+			[
+				[6, 14, 6, 19],
+				[7, 14, 7, 19],
+				[9, 14, 9, 19]
+			]
+		);
+
+		findModel.replaceAll();
+		assertFindState(
+			editor,
+			[1, 1, 1, 1],
+			null,
+			[]
+		);
+		assert.equal(editor.getModel().getLineContent(6), '    cout << "hi world, Hello!" << endl;');
+		assert.equal(editor.getModel().getLineContent(7), '    cout << "hi world again" << endl;');
+		assert.equal(editor.getModel().getLineContent(9), '    cout << "hiworld again" << endl;');
+
+		findModel.dispose();
+		findState.dispose();
+	});
 });
diff --git a/src/vs/editor/contrib/find/test/common/replacePattern.test.ts b/src/vs/editor/contrib/find/test/common/replacePattern.test.ts
index 88fcaeeb3aa83d4d0f896dd5b801c4f2ff82b952..63105b824384846d515e8d9a81b69d21abf2ac25 100644
--- a/src/vs/editor/contrib/find/test/common/replacePattern.test.ts
+++ b/src/vs/editor/contrib/find/test/common/replacePattern.test.ts
@@ -147,4 +147,11 @@ suite('Replace Pattern test', () => {
 		assertReplace('this is a bla text', /b(la)(?=\stext$)/, 'f$0', 'fbla');
 		assertReplace('this is a bla text', /b(la)(?=\stext$)/, '$0ah', 'blaah');
 	});
+
+	test('issue #19740 Find and replace capture group/backreference inserts `undefined` instead of empty string', () => {
+		let replacePattern = parseReplaceString('a{$1}');
+		let matches = /a(z)?/.exec('abcd');
+		let actual = replacePattern.buildReplaceString(matches);
+		assert.equal(actual, 'a{}');
+	});
 });