diff --git a/rules/custom-error-definition.js b/rules/custom-error-definition.js
index c5e47d69d0..b9081e9b75 100644
--- a/rules/custom-error-definition.js
+++ b/rules/custom-error-definition.js
@@ -54,12 +54,15 @@ const isAssignmentExpression = (node, name) => {
 	return lhs.property.name === name;
 };
 
-const isClassProperty = (node, name) => {
-	if (node.type !== 'ClassProperty' || node.computed) {
+const isPropertyDefinition = (node, name) => {
+	const {type, computed, key} = node;
+	if (type !== 'PropertyDefinition' && type !== 'ClassProperty') {
 		return false;
 	}
 
-	const {key} = node;
+	if (computed) {
+		return false;
+	}
 
 	if (key.type !== 'Identifier') {
 		return false;
@@ -144,7 +147,7 @@ const customErrorDefinition = (context, node) => {
 
 	const nameExpression = constructorBody.find(x => isAssignmentExpression(x, 'name'));
 	if (!nameExpression) {
-		const nameProperty = body.find(node => isClassProperty(node, 'name'));
+		const nameProperty = body.find(node => isPropertyDefinition(node, 'name'));
 
 		if (!nameProperty || !nameProperty.value || nameProperty.value.value !== name) {
 			context.report({
diff --git a/rules/no-static-only-class.js b/rules/no-static-only-class.js
index dc02da42f6..afdbc63b9b 100644
--- a/rules/no-static-only-class.js
+++ b/rules/no-static-only-class.js
@@ -23,9 +23,14 @@ const isDeclarationOfExportDefaultDeclaration = node =>
 	node.parent.type === 'ExportDefaultDeclaration' &&
 	node.parent.declaration === node;
 
+// https://github.com/estree/estree/blob/master/stage3/class-features.md#propertydefinition
+const isPropertyDefinition = node => node.type === 'PropertyDefinition' ||
+	// Legacy node type
+	node.type === 'ClassProperty';
+const isMethodDefinition = node => node.type === 'MethodDefinition';
+
 function isStaticMember(node) {
 	const {
-		type,
 		private: isPrivate,
 		static: isStatic,
 		declare: isDeclare,
@@ -37,7 +42,7 @@ function isStaticMember(node) {
 
 	// Avoid matching unexpected node. For example: https://github.com/tc39/proposal-class-static-block
 	/* istanbul ignore next */
-	if (type !== 'ClassProperty' && type !== 'MethodDefinition') {
+	if (!isPropertyDefinition(node) && !isMethodDefinition(node)) {
 		return false;
 	}
 
@@ -60,8 +65,6 @@ function isStaticMember(node) {
 }
 
 function * switchClassMemberToObjectProperty(node, sourceCode, fixer) {
-	const {type} = node;
-
 	const staticToken = sourceCode.getFirstToken(node);
 	assertToken(staticToken, {
 		expected: [
@@ -75,12 +78,12 @@ function * switchClassMemberToObjectProperty(node, sourceCode, fixer) {
 	yield fixer.remove(staticToken);
 	yield removeSpacesAfter(staticToken, sourceCode, fixer);
 
-	const maybeSemicolonToken = type === 'ClassProperty' ?
+	const maybeSemicolonToken = isPropertyDefinition(node) ?
 		sourceCode.getLastToken(node) :
 		sourceCode.getTokenAfter(node);
 	const hasSemicolonToken = isSemicolonToken(maybeSemicolonToken);
 
-	if (type === 'ClassProperty') {
+	if (isPropertyDefinition(node)) {
 		const {key, value} = node;
 
 		if (value) {
@@ -132,11 +135,11 @@ function switchClassToObject(node, sourceCode) {
 
 	for (const node of body.body) {
 		if (
-			node.type === 'ClassProperty' &&
+			isPropertyDefinition(node) &&
 			(
 				node.typeAnnotation ||
-				// This is a stupid way to check if `value` of `ClassProperty` uses `this`
-				(node.value && sourceCode.getText(node).includes('this'))
+				// This is a stupid way to check if `value` of `PropertyDefinition` uses `this`
+				(node.value && sourceCode.getText(node.value).includes('this'))
 			)
 		) {
 			return;
diff --git a/rules/prevent-abbreviations.js b/rules/prevent-abbreviations.js
index b78193c45d..377e05f069 100644
--- a/rules/prevent-abbreviations.js
+++ b/rules/prevent-abbreviations.js
@@ -538,7 +538,7 @@ const shouldReportIdentifierAsProperty = identifier => {
 	}
 
 	if (
-		identifier.parent.type === 'ClassProperty' &&
+		(identifier.parent.type === 'ClassProperty' || identifier.parent.type === 'PropertyDefinition') &&
 		identifier.parent.key === identifier &&
 		!identifier.parent.computed
 	) {
diff --git a/test/custom-error-definition.mjs b/test/custom-error-definition.mjs
index 591e15c5b6..933df282ae 100644
--- a/test/custom-error-definition.mjs
+++ b/test/custom-error-definition.mjs
@@ -504,6 +504,28 @@ runTest.babel({
 				}
 			`,
 			errors: [invalidNameError('ValidationError')]
+		},
+		// `computed`
+		{
+			code: outdent`
+				const name = 'computed-name';
+				class FooError extends Error {
+					[name] = 'FooError';
+					constructor(message) {
+						super(message);
+					}
+				}
+			`,
+			output: outdent`
+				const name = 'computed-name';
+				class FooError extends Error {
+					[name] = 'FooError';
+					constructor(message) {
+						super(message);
+					}
+				}
+			`,
+			errors: [invalidNameError('FooError')]
 		}
 	]
 });
diff --git a/test/no-static-only-class.mjs b/test/no-static-only-class.mjs
index bddf6c3dcf..e654ef1400 100644
--- a/test/no-static-only-class.mjs
+++ b/test/no-static-only-class.mjs
@@ -175,6 +175,12 @@ test.typescript({
 				static b = this.a;
 			}
 		`),
+		// `this` in `key` should fixable
+		{
+			code: 'class A {static [this.a] = 1}',
+			output: 'const A = {[this.a] : 1,};',
+			errors: 1
+		},
 		// This case should be fixable, but we simply check code of value includes `this`
 		noFixingCase(outdent`
 			class A {
diff --git a/test/utils/test.mjs b/test/utils/test.mjs
index 86401ff724..e86326a07b 100644
--- a/test/utils/test.mjs
+++ b/test/utils/test.mjs
@@ -45,7 +45,13 @@ class Tester {
 		testerOptions.parserOptions = testerOptions.parserOptions || {};
 		testerOptions.parserOptions.babelOptions = testerOptions.parserOptions.babelOptions || {};
 		testerOptions.parserOptions.babelOptions.parserOpts = testerOptions.parserOptions.babelOptions.parserOpts || {};
-		testerOptions.parserOptions.babelOptions.parserOpts.plugins = testerOptions.parserOptions.babelOptions.parserOpts.plugins || [];
+		let babelPlugins = testerOptions.parserOptions.babelOptions.parserOpts.plugins || [];
+		babelPlugins = [
+			['estree', {classFeatures: true}],
+			'jsx',
+			'classProperties',
+			...babelPlugins
+		];
 
 		return this.runTest({
 			...tests,
@@ -62,11 +68,7 @@ class Tester {
 						...testerOptions.parserOptions.babelOptions,
 						parserOpts: {
 							...testerOptions.parserOptions.babelOptions.parserOpts,
-							plugins: [
-								'jsx',
-								'classProperties',
-								...testerOptions.parserOptions.babelOptions.parserOpts.plugins
-							]
+							plugins: babelPlugins
 						}
 					}
 				}