diff --git a/src/main/java/org/codehaus/groovy/transform/stc/StaticTypeCheckingVisitor.java b/src/main/java/org/codehaus/groovy/transform/stc/StaticTypeCheckingVisitor.java
index f13b9a36446..13b2ef33f4f 100644
--- a/src/main/java/org/codehaus/groovy/transform/stc/StaticTypeCheckingVisitor.java
+++ b/src/main/java/org/codehaus/groovy/transform/stc/StaticTypeCheckingVisitor.java
@@ -2517,6 +2517,10 @@ && getType(nameExpr).equals(STRING_TYPE)) {
                 if (isClassClassNodeWrappingConcreteType(type)){
                     type = type.getGenericsTypes()[0].getType();
                     storeType(expression,wrapClosureType(type));
+                    // GROOVY-11385: check if create possible
+                    if (type.isAbstract() && !type.isArray())
+                        addStaticTypeError("Cannot instantiate the type " +
+                                    prettyPrintTypeName(type), expression);
                 }
                 return;
             }
diff --git a/src/test/groovy/transform/stc/MethodReferenceTest.groovy b/src/test/groovy/transform/stc/MethodReferenceTest.groovy
index 501aea0ff86..f9c8735187a 100644
--- a/src/test/groovy/transform/stc/MethodReferenceTest.groovy
+++ b/src/test/groovy/transform/stc/MethodReferenceTest.groovy
@@ -1034,6 +1034,35 @@ final class MethodReferenceTest {
         '''
     }
 
+    @Test // class::new -- GROOVY-11385
+    void testFunctionCN8() {
+        def err = shouldFail imports + '''
+            abstract class A {
+                A(String s) {}
+            }
+            @CompileStatic
+            void test() {
+                Function<String, A> f = A::new
+                f.apply("") // InstantiationException
+            }
+
+            test()
+        '''
+        assert err =~ /Cannot instantiate the type A/
+
+        for (op in ['::','.&']) {
+            err = shouldFail imports + """
+                @CompileStatic
+                void test() {
+                    Supplier<Number> s = Number${op}new
+                }
+
+                test()
+            """
+            assert err =~ /Cannot instantiate the type java.lang.Number/
+        }
+    }
+
     @Test // arrayClass::new
     void testIntFunctionCN() {
         assertScript imports + '''