diff --git a/python/src/com/jetbrains/python/codeInsight/typing/PyTypingTypeProvider.java b/python/src/com/jetbrains/python/codeInsight/typing/PyTypingTypeProvider.java
index b7900b73461b..9ec2fe8ac819 100644
--- a/python/src/com/jetbrains/python/codeInsight/typing/PyTypingTypeProvider.java
+++ b/python/src/com/jetbrains/python/codeInsight/typing/PyTypingTypeProvider.java
@@ -36,6 +36,7 @@ import com.jetbrains.python.codeInsight.functionTypeComments.psi.PyFunctionTypeA
 import com.jetbrains.python.codeInsight.functionTypeComments.psi.PyFunctionTypeAnnotationFile;
 import com.jetbrains.python.codeInsight.functionTypeComments.psi.PyParameterTypeList;
 import com.jetbrains.python.psi.*;
+import com.jetbrains.python.psi.impl.PyBuiltinCache;
 import com.jetbrains.python.psi.impl.PyExpressionCodeFragmentImpl;
 import com.jetbrains.python.psi.resolve.PyResolveContext;
 import com.jetbrains.python.psi.resolve.PyResolveImportUtil;
@@ -63,6 +64,7 @@ public class PyTypingTypeProvider extends PyTypeProviderBase {
   public static final String NAMEDTUPLE = "typing.NamedTuple";
   public static final String GENERIC = "typing.Generic";
   public static final String TYPE = "typing.Type";
+  public static final String ANY = "typing.Any";
 
   public static final Pattern TYPE_COMMENT_PATTERN = Pattern.compile("# *type: *(.*)");
 
@@ -471,9 +473,9 @@ public class PyTypingTypeProvider extends PyTypeProviderBase {
       if (callableType != null) {
         return Ref.create(callableType);
       }
-      final PyType classObjType = getClassObjectType(resolved, context);
+      final Ref<PyType> classObjType = getClassObjectType(resolved, context);
       if (classObjType != null) {
-        return Ref.create(classObjType);
+        return classObjType;
       }
       final PyType parameterizedType = getParameterizedType(resolved, context);
       if (parameterizedType != null) {
@@ -507,7 +509,7 @@ public class PyTypingTypeProvider extends PyTypeProviderBase {
   }
 
   @Nullable
-  private static PyType getClassObjectType(@NotNull PsiElement resolved, @NotNull Context context) {
+  private static Ref<PyType> getClassObjectType(@NotNull PsiElement resolved, @NotNull Context context) {
     if (resolved instanceof PySubscriptionExpression) {
       final PySubscriptionExpression subsExpr = (PySubscriptionExpression)resolved;
       final PyExpression operand = subsExpr.getOperand();
@@ -515,32 +517,33 @@ public class PyTypingTypeProvider extends PyTypeProviderBase {
       if (operandNames.contains(TYPE)) {
         final PyExpression indexExpr = subsExpr.getIndexExpression();
         if (indexExpr != null) {
+          if (resolveToQualifiedNames(indexExpr, context.getTypeContext()).contains(ANY)) {
+            return Ref.create(PyBuiltinCache.getInstance(resolved).getTypeType());
+          }
           final PyType type = Ref.deref(getType(indexExpr, context));
           final PyClassType classType = as(type, PyClassType.class);
           if (classType != null && !classType.isDefinition()) {
-            return new PyClassTypeImpl(classType.getPyClass(), true);
+            return Ref.create(new PyClassTypeImpl(classType.getPyClass(), true));
           }
           final PyGenericType typeVar = as(type, PyGenericType.class);
           if (typeVar != null && !typeVar.isDefinition()) {
-            return new PyGenericType(typeVar.getName(), typeVar.getBound(), true);
+            return Ref.create(new PyGenericType(typeVar.getName(), typeVar.getBound(), true));
           }
         }
+        // Map Type[Something] with unsupported type parameter to Any, instead of generic type for the class "type"
+        return Ref.create();
       }
     }
     // Replace plain non-parametrized Type with its builtin counterpart
     else if (TYPE.equals(getQualifiedName(resolved))) {
-      return PyTypeParser.getTypeByName(resolved, PyNames.TYPE);
+      return Ref.create(PyBuiltinCache.getInstance(resolved).getTypeType());
     }
     return null;
   }
 
   @Nullable
   private static Ref<PyType> getAnyType(@NotNull PsiElement element) {
-    final PyQualifiedNameOwner qualifiedNameOwner = as(element, PyQualifiedNameOwner.class);
-    if (qualifiedNameOwner != null && "typing.Any".equals(qualifiedNameOwner.getQualifiedName())) {
-      return Ref.create();
-    }
-    return null;
+    return ANY.equals(getQualifiedName(element)) ? Ref.create() : null;
   }
 
   @Nullable
diff --git a/python/testData/inspections/PyTypeCheckerInspection/TypeAndClassObjectTypesCompatibility.py b/python/testData/inspections/PyTypeCheckerInspection/TypeAndClassObjectTypesCompatibility.py
index b484b262720f..cc0be1130066 100644
--- a/python/testData/inspections/PyTypeCheckerInspection/TypeAndClassObjectTypesCompatibility.py
+++ b/python/testData/inspections/PyTypeCheckerInspection/TypeAndClassObjectTypesCompatibility.py
@@ -12,6 +12,10 @@ def expects_typing_type(x: Type):
     expects_type(x)
 
 
+def expects_typing_type_any(x: Type[Any]):
+    expects_type(x)
+
+
 def expects_any_type_via_type_var(x: Type[T]):
     expects_type(x)
 
@@ -31,6 +35,7 @@ def expects_object(x: object):
 expects_type(type)
 expects_type(object)
 expects_typing_type(type)
+expects_typing_type_any(type)
 expects_typing_type(object)
 expects_str_class(<warning descr="Expected type 'Type[str]', got 'type' instead">type</warning>)
 expects_any_type_via_type_var(type)
diff --git a/python/testSrc/com/jetbrains/python/PyTypingTest.java b/python/testSrc/com/jetbrains/python/PyTypingTest.java
index d33fa8a7e5ea..84ac1a202199 100644
--- a/python/testSrc/com/jetbrains/python/PyTypingTest.java
+++ b/python/testSrc/com/jetbrains/python/PyTypingTest.java
@@ -840,6 +840,24 @@ public class PyTypingTest extends PyTestCase {
            "def f(x: Type):\n" +
            "    expr = x");
   }
+  
+  // PY-20057
+  public void testTypingTypeOfAnyMapsToBuiltinType() {
+    doTest("type",
+           "from typing import Type, Any\n" +
+           "\n" +
+           "def f(x: Type[Any]):\n" +
+           "    expr = x");
+  }
+
+  // PY-20057
+  public void testIllegalTypingTypeFormat() {
+    doTest("Tuple[Any, Any, Any]",
+           "from typing import Type, Tuple\n" +
+           "\n" +
+           "def f(x: Tuple[Type[42], Type[], Type[unresolved]]):\n" +
+           "    expr = x");
+  }
 
   private void doTestNoInjectedText(@NotNull String text) {
     myFixture.configureByText(PythonFileType.INSTANCE, text);