diff --git a/src/rules/__tests__/prefer-to-be.test.ts b/src/rules/__tests__/prefer-to-be.test.ts
index 3b9a6ac0a..5b810b061 100644
--- a/src/rules/__tests__/prefer-to-be.test.ts
+++ b/src/rules/__tests__/prefer-to-be.test.ts
@@ -1,7 +1,13 @@
 import { TSESLint } from '@typescript-eslint/experimental-utils';
 import rule from '../prefer-to-be';
+import { espreeParser } from './test-utils';
 
-const ruleTester = new TSESLint.RuleTester();
+const ruleTester = new TSESLint.RuleTester({
+  parser: espreeParser,
+  parserOptions: {
+    ecmaVersion: 2015,
+  },
+});
 
 ruleTester.run('prefer-to-be', rule, {
   valid: [
@@ -16,6 +22,7 @@ ruleTester.run('prefer-to-be', rule, {
     'expect("something");',
     'expect(token).toStrictEqual(/[abc]+/g);',
     "expect(token).toStrictEqual(new RegExp('[abc]+', 'g'));",
+    'expect(value).toEqual(dedent`my string`);',
   ],
   invalid: [
     {
@@ -33,6 +40,16 @@ ruleTester.run('prefer-to-be', rule, {
       output: 'expect(value).toBe(1);',
       errors: [{ messageId: 'useToBe', column: 15, line: 1 }],
     },
+    {
+      code: 'expect(value).toEqual(`my string`);',
+      output: 'expect(value).toBe(`my string`);',
+      errors: [{ messageId: 'useToBe', column: 15, line: 1 }],
+    },
+    {
+      code: 'expect(value).toStrictEqual(`my ${string}`);',
+      output: 'expect(value).toBe(`my ${string}`);',
+      errors: [{ messageId: 'useToBe', column: 15, line: 1 }],
+    },
     {
       code: 'expect(loadMessage()).resolves.toStrictEqual("hello world");',
       output: 'expect(loadMessage()).resolves.toBe("hello world");',
diff --git a/src/rules/prefer-to-be.ts b/src/rules/prefer-to-be.ts
index 165a129d7..f45e814fd 100644
--- a/src/rules/prefer-to-be.ts
+++ b/src/rules/prefer-to-be.ts
@@ -35,10 +35,16 @@ const isFirstArgumentIdentifier = (
   name: string,
 ) => isIdentifier(getFirstArgument(matcher), name);
 
-const isPrimitiveLiteral = (matcher: ParsedEqualityMatcherCall): boolean => {
+const shouldUseToBe = (matcher: ParsedEqualityMatcherCall): boolean => {
   const firstArg = getFirstArgument(matcher);
 
-  return firstArg.type === AST_NODE_TYPES.Literal && !('regex' in firstArg);
+  if (firstArg.type === AST_NODE_TYPES.Literal) {
+    // regex literals are classed as literals, but they're actually objects
+    // which means "toBe" will give different results than other matchers
+    return !('regex' in firstArg);
+  }
+
+  return firstArg.type === AST_NODE_TYPES.TemplateLiteral;
 };
 
 const getFirstArgument = (matcher: ParsedEqualityMatcherCall) => {
@@ -164,10 +170,7 @@ export default createRule({
           return;
         }
 
-        if (
-          isPrimitiveLiteral(matcher) &&
-          matcher.name !== EqualityMatcher.toBe
-        ) {
+        if (shouldUseToBe(matcher) && matcher.name !== EqualityMatcher.toBe) {
           reportPreferToBe(context, '', matcher);
         }
       },