diff --git a/pkg/_fe_analyzer_shared/lib/src/exhaustiveness/types/enum.dart b/pkg/_fe_analyzer_shared/lib/src/exhaustiveness/types/enum.dart
index d2e73739be8..be3becaf8df 100644
--- a/pkg/_fe_analyzer_shared/lib/src/exhaustiveness/types/enum.dart
+++ b/pkg/_fe_analyzer_shared/lib/src/exhaustiveness/types/enum.dart
@@ -17,7 +17,7 @@ abstract class EnumOperations<Type extends Object, EnumClass extends Object,
   /// Returns the value defined by the [enumElement]. The encoding is specific
   /// the implementation of this interface but must ensure constant value
   /// identity.
-  EnumElementValue getEnumElementValue(EnumElement enumElement);
+  EnumElementValue? getEnumElementValue(EnumElement enumElement);
 
   /// Returns the declared name of the [enumElement].
   String getEnumElementName(EnumElement enumElement);
@@ -57,14 +57,16 @@ class EnumInfo<Type extends Object, EnumClass extends Object,
     Map<EnumElementValue, EnumElementStaticType<Type, EnumElement>> elements =
         {};
     for (EnumElement element in _enumOperations.getEnumElements(_enumClass)) {
-      EnumElementValue value = _enumOperations.getEnumElementValue(element);
-      elements[value] = new EnumElementStaticType<Type, EnumElement>(
-          _typeOperations,
-          _fieldLookup,
-          _enumOperations.getEnumElementType(element),
-          new IdentityRestriction<EnumElement>(element),
-          _enumOperations.getEnumElementName(element),
-          element);
+      EnumElementValue? value = _enumOperations.getEnumElementValue(element);
+      if (value != null) {
+        elements[value] = new EnumElementStaticType<Type, EnumElement>(
+            _typeOperations,
+            _fieldLookup,
+            _enumOperations.getEnumElementType(element),
+            new IdentityRestriction<EnumElement>(element),
+            _enumOperations.getEnumElementName(element),
+            element);
+      }
     }
     return elements;
   }
diff --git a/pkg/analyzer/lib/src/generated/exhaustiveness.dart b/pkg/analyzer/lib/src/generated/exhaustiveness.dart
index 08eec6ff422..1976aec3c50 100644
--- a/pkg/analyzer/lib/src/generated/exhaustiveness.dart
+++ b/pkg/analyzer/lib/src/generated/exhaustiveness.dart
@@ -56,8 +56,8 @@ class AnalyzerEnumOperations
   }
 
   @override
-  DartObject getEnumElementValue(FieldElement enumField) {
-    return enumField.computeConstantValue()!;
+  DartObject? getEnumElementValue(FieldElement enumField) {
+    return enumField.computeConstantValue();
   }
 }
 
diff --git a/pkg/analyzer/test/src/diagnostics/non_exhaustive_switch_test.dart b/pkg/analyzer/test/src/diagnostics/non_exhaustive_switch_test.dart
index ce1a4c2a949..2aecdca3a54 100644
--- a/pkg/analyzer/test/src/diagnostics/non_exhaustive_switch_test.dart
+++ b/pkg/analyzer/test/src/diagnostics/non_exhaustive_switch_test.dart
@@ -239,6 +239,26 @@ void f(E x) {
     );
   }
 
+  test_alwaysExhaustive_enum_cannotCompute() async {
+    await assertErrorsInCode(r'''
+enum E {
+  v1(v2), v2(v1);
+  const E(Object f);
+}
+
+void f(E x) {
+  switch (x) {
+    case E.v1:
+    case E.v2:
+      break;
+  }
+}
+''', [
+      error(CompileTimeErrorCode.RECURSIVE_COMPILE_TIME_CONSTANT, 11, 2),
+      error(CompileTimeErrorCode.RECURSIVE_COMPILE_TIME_CONSTANT, 19, 2),
+    ]);
+  }
+
   test_alwaysExhaustive_Null_hasError() async {
     await assertErrorsInCode(r'''
 void f(Null x) {