diff --git a/packages/eslint-plugin/src/rules/adjacent-overload-signatures.ts b/packages/eslint-plugin/src/rules/adjacent-overload-signatures.ts
index 7007b1c3bdf..8e864c9c4a2 100644
--- a/packages/eslint-plugin/src/rules/adjacent-overload-signatures.ts
+++ b/packages/eslint-plugin/src/rules/adjacent-overload-signatures.ts
@@ -26,6 +26,8 @@ export default util.createRule({
   },
   defaultOptions: [],
   create(context) {
+    const sourceCode = context.getSourceCode();
+
     /**
      * Gets the name of the member being processed.
      * @param member the member being processed.
@@ -57,7 +59,7 @@ export default util.createRule({
         case AST_NODE_TYPES.TSConstructSignatureDeclaration:
           return 'new';
         case AST_NODE_TYPES.MethodDefinition:
-          return util.getNameFromPropertyName(member.key);
+          return util.getNameFromClassMember(member, sourceCode);
       }
 
       return null;
diff --git a/packages/eslint-plugin/src/rules/explicit-member-accessibility.ts b/packages/eslint-plugin/src/rules/explicit-member-accessibility.ts
index afae022c262..66029faa501 100644
--- a/packages/eslint-plugin/src/rules/explicit-member-accessibility.ts
+++ b/packages/eslint-plugin/src/rules/explicit-member-accessibility.ts
@@ -20,6 +20,7 @@ export default util.createRule({
   },
   defaultOptions: [],
   create(context) {
+    const sourceCode = context.getSourceCode();
     /**
      * Checks if a method declaration has an accessibility modifier.
      * @param methodDefinition The node representing a MethodDefinition.
@@ -36,7 +37,7 @@ export default util.createRule({
           messageId: 'missingAccessibility',
           data: {
             type: 'method definition',
-            name: util.getNameFromPropertyName(methodDefinition.key),
+            name: util.getNameFromClassMember(methodDefinition, sourceCode),
           },
         });
       }
diff --git a/packages/eslint-plugin/src/rules/member-naming.ts b/packages/eslint-plugin/src/rules/member-naming.ts
index 23c14c8b39c..2efdf6ea307 100644
--- a/packages/eslint-plugin/src/rules/member-naming.ts
+++ b/packages/eslint-plugin/src/rules/member-naming.ts
@@ -51,6 +51,8 @@ export default util.createRule<Options, MessageIds>({
   },
   defaultOptions: [{}],
   create(context, [config]) {
+    const sourceCode = context.getSourceCode();
+
     const conventions = (Object.keys(config) as Modifiers[]).reduce<
       Config<RegExp>
     >((acc, accessibility) => {
@@ -69,7 +71,7 @@ export default util.createRule<Options, MessageIds>({
     function validateName(
       node: TSESTree.MethodDefinition | TSESTree.ClassProperty,
     ): void {
-      const name = util.getNameFromPropertyName(node.key);
+      const name = util.getNameFromClassMember(node, sourceCode);
       const accessibility: Modifiers = node.accessibility || 'public';
       const convention = conventions[accessibility];
 
diff --git a/packages/eslint-plugin/src/rules/member-ordering.ts b/packages/eslint-plugin/src/rules/member-ordering.ts
index dff4752bab4..f3ae6a439bd 100644
--- a/packages/eslint-plugin/src/rules/member-ordering.ts
+++ b/packages/eslint-plugin/src/rules/member-ordering.ts
@@ -164,6 +164,8 @@ export default util.createRule<Options, MessageIds>({
     },
   ],
   create(context, [options]) {
+    const sourceCode = context.getSourceCode();
+
     const functionExpressions = [
       AST_NODE_TYPES.FunctionExpression,
       AST_NODE_TYPES.ArrowFunctionExpression,
@@ -213,7 +215,7 @@ export default util.createRule<Options, MessageIds>({
         case AST_NODE_TYPES.MethodDefinition:
           return node.kind === 'constructor'
             ? 'constructor'
-            : util.getNameFromPropertyName(node.key);
+            : util.getNameFromClassMember(node, sourceCode);
         case AST_NODE_TYPES.TSConstructSignatureDeclaration:
           return 'new';
         default:
diff --git a/packages/eslint-plugin/src/util/misc.ts b/packages/eslint-plugin/src/util/misc.ts
index dbaaebc3f7a..ab56cd4e694 100644
--- a/packages/eslint-plugin/src/util/misc.ts
+++ b/packages/eslint-plugin/src/util/misc.ts
@@ -4,6 +4,7 @@
 
 import { TSESTree, AST_NODE_TYPES } from '@typescript-eslint/typescript-estree';
 import RuleModule from 'ts-eslint';
+import { SourceCode } from 'ts-eslint';
 
 /**
  * Check if the context file name is *.ts or *.tsx
@@ -63,3 +64,31 @@ export function getNameFromPropertyName(
   }
   return `${propertyName.value}`;
 }
+
+/**
+ * Gets a string name representation of the name of the given MethodDefinition
+ * or ClassProperty node, with handling for computed property names.
+ */
+export function getNameFromClassMember(
+  methodDefinition: TSESTree.MethodDefinition | TSESTree.ClassProperty,
+  sourceCode: SourceCode,
+): string {
+  if (keyCanBeReadAsPropertyName(methodDefinition.key)) {
+    return getNameFromPropertyName(methodDefinition.key);
+  }
+
+  return sourceCode.text.slice(...methodDefinition.key.range);
+}
+
+/**
+ * This covers both actual property names, as well as computed properties that are either
+ * an identifier or a literal at the top level.
+ */
+function keyCanBeReadAsPropertyName(
+  node: TSESTree.Expression,
+): node is TSESTree.PropertyName {
+  return (
+    node.type === AST_NODE_TYPES.Literal ||
+    node.type === AST_NODE_TYPES.Identifier
+  );
+}
diff --git a/packages/eslint-plugin/tests/rules/adjacent-overload-signatures.test.ts b/packages/eslint-plugin/tests/rules/adjacent-overload-signatures.test.ts
index 01680fef838..c040362a128 100644
--- a/packages/eslint-plugin/tests/rules/adjacent-overload-signatures.test.ts
+++ b/packages/eslint-plugin/tests/rules/adjacent-overload-signatures.test.ts
@@ -217,6 +217,11 @@ class Test {
     // examples from https://github.com/nzakas/eslint-plugin-typescript/issues/138
     'export default function<T>(foo : T) {}',
     'export default function named<T>(foo : T) {}',
+    `
+interface Foo {
+  [Symbol.toStringTag](): void;
+  [Symbol.iterator](): void;
+}`,
   ],
   invalid: [
     {
diff --git a/packages/eslint-plugin/typings/ts-eslint.d.ts b/packages/eslint-plugin/typings/ts-eslint.d.ts
index 998c6958342..b757a1b5982 100644
--- a/packages/eslint-plugin/typings/ts-eslint.d.ts
+++ b/packages/eslint-plugin/typings/ts-eslint.d.ts
@@ -683,6 +683,7 @@ declare module 'ts-eslint' {
     RuleMetaData,
     RuleMetaDataDocs,
     Scope,
+    SourceCode,
   };
   export default RuleModule;
 }
diff --git a/packages/typescript-estree/src/ts-estree/ts-estree.ts b/packages/typescript-estree/src/ts-estree/ts-estree.ts
index 4a9c7b91ae1..f15f50abca3 100644
--- a/packages/typescript-estree/src/ts-estree/ts-estree.ts
+++ b/packages/typescript-estree/src/ts-estree/ts-estree.ts
@@ -500,7 +500,7 @@ interface LiteralBase extends BaseNode {
 }
 
 interface MethodDefinitionBase extends BaseNode {
-  key: PropertyName;
+  key: Expression;
   value: FunctionExpression | TSEmptyBodyFunctionExpression;
   computed: boolean;
   static: boolean;