diff --git a/packages/eslint-plugin/src/rules/no-type-alias.ts b/packages/eslint-plugin/src/rules/no-type-alias.ts
index f260d124133f..344d0391f281 100644
--- a/packages/eslint-plugin/src/rules/no-type-alias.ts
+++ b/packages/eslint-plugin/src/rules/no-type-alias.ts
@@ -239,9 +239,6 @@ export default util.createRule<Options, MessageIds>({
         ) {
           reportError(type.node, type.compositionType, isTopLevel, 'Aliases');
         }
-      } else {
-        // unhandled type - shouldn't happen
-        reportError(type.node, type.compositionType, isTopLevel, 'Unhandled');
       }
     }
 
diff --git a/packages/eslint-plugin/tests/rules/no-type-alias.test.ts b/packages/eslint-plugin/tests/rules/no-type-alias.test.ts
index 3c3d83520e8f..b02f43378aea 100644
--- a/packages/eslint-plugin/tests/rules/no-type-alias.test.ts
+++ b/packages/eslint-plugin/tests/rules/no-type-alias.test.ts
@@ -7,6 +7,18 @@ const ruleTester = new RuleTester({
 
 ruleTester.run('no-type-alias', rule, {
   valid: [
+    {
+      code: 'type Foo = string | [number, number];',
+      options: [{ allowAliases: 'in-unions' }],
+    },
+    {
+      code: 'type Foo = string & [number, number];',
+      options: [{ allowAliases: 'in-intersections' }],
+    },
+    {
+      code: 'type Foo = string & [number, number] | [number, number, number];',
+      options: [{ allowAliases: 'in-unions-and-intersections' }],
+    },
     {
       code: "type A = 'a' & ('b' | 'c');",
       options: [{ allowAliases: 'always' }],