diff --git a/compiler/src/dotty/tools/dotc/core/Definitions.scala b/compiler/src/dotty/tools/dotc/core/Definitions.scala
index 547ceb292055..2fec0683c410 100644
--- a/compiler/src/dotty/tools/dotc/core/Definitions.scala
+++ b/compiler/src/dotty/tools/dotc/core/Definitions.scala
@@ -1196,6 +1196,8 @@ class Definitions {
 
   @tu lazy val topClasses: Set[Symbol] = Set(AnyClass, MatchableClass, ObjectClass, AnyValClass)
 
+  @tu lazy val untestableClasses: Set[Symbol] = Set(NothingClass, NullClass, SingletonClass)
+
   @tu lazy val AbstractFunctionType: Array[TypeRef] = mkArityArray("scala.runtime.AbstractFunction", MaxImplementedFunctionArity, 0)
   val AbstractFunctionClassPerRun: PerRun[Array[Symbol]] = new PerRun(AbstractFunctionType.map(_.symbol.asClass))
   def AbstractFunctionClass(n: Int)(using Context): Symbol = AbstractFunctionClassPerRun()(using ctx)(n)
diff --git a/compiler/src/dotty/tools/dotc/transform/TypeTestsCasts.scala b/compiler/src/dotty/tools/dotc/transform/TypeTestsCasts.scala
index 5d03d5381eed..a4951b99f599 100644
--- a/compiler/src/dotty/tools/dotc/transform/TypeTestsCasts.scala
+++ b/compiler/src/dotty/tools/dotc/transform/TypeTestsCasts.scala
@@ -339,8 +339,14 @@ object TypeTestsCasts {
           case AppliedType(tref: TypeRef, _) if tref.symbol == defn.PairClass =>
             ref(defn.RuntimeTuples_isInstanceOfNonEmptyTuple).appliedTo(expr)
           case _ =>
-            val erasedTestType = erasure(testType)
-            transformIsInstanceOf(expr, erasedTestType, erasedTestType, flagUnrelated)
+            val testWidened = testType.widen
+            defn.untestableClasses.find(testWidened.isRef(_)) match
+              case Some(untestable) =>
+                report.error(i"$untestable cannot be used in runtime type tests", tree.srcPos)
+                constant(expr, Literal(Constant(false)))
+              case _ =>
+                val erasedTestType = erasure(testType)
+                transformIsInstanceOf(expr, erasedTestType, erasedTestType, flagUnrelated)
         }
 
         if (sym.isTypeTest) {
diff --git a/tests/explicit-nulls/pos/matchable.scala b/tests/explicit-nulls/pos/matchable.scala
index 928f8e33934f..ef9c5e7eae07 100644
--- a/tests/explicit-nulls/pos/matchable.scala
+++ b/tests/explicit-nulls/pos/matchable.scala
@@ -1,3 +1 @@
-def foo1[T <: Matchable](t: T) = t match { case t: Null => () }
-
 def foo2[T <: Matchable](t: T) = t match { case null => () }
\ No newline at end of file
diff --git a/tests/neg/i4004.scala b/tests/neg/i4004.scala
new file mode 100644
index 000000000000..bf757a0863a7
--- /dev/null
+++ b/tests/neg/i4004.scala
@@ -0,0 +1,16 @@
+@main def Test =
+  "a".isInstanceOf[Null] // error
+  null.isInstanceOf[Null] // error
+  "a".isInstanceOf[Nothing] // error
+  "a".isInstanceOf[Singleton] // error
+
+  "a" match
+  case _: Null => () // error
+  case _: Nothing => () // error
+  case _: Singleton => () // error
+  case _ => ()
+
+  null match
+  case _: Null => () // error
+  case _ => ()
+