diff --git a/src/pystencils/backend/kernelcreation/freeze.py b/src/pystencils/backend/kernelcreation/freeze.py
index 25ce2811516ae361fc8efc074686f64f762e89ab..3f1ca8ede5b35f93bcb7898788d7718f063af1d4 100644
--- a/src/pystencils/backend/kernelcreation/freeze.py
+++ b/src/pystencils/backend/kernelcreation/freeze.py
@@ -58,7 +58,7 @@ from ..ast.expressions import (
 )
 
 from ..constants import PsConstant
-from ...types import PsStructType, PsType
+from ...types import PsNumericType, PsStructType, PsType
 from ..exceptions import PsInputError
 from ..functions import PsMathFunction, MathFunctions
 
@@ -462,7 +462,7 @@ class FreezeExpressions:
             ]
         return cast(PsCall, args[0])
 
-    def map_CastFunc(self, cast_expr: CastFunc) -> PsCast:
+    def map_CastFunc(self, cast_expr: CastFunc) -> PsCast | PsConstantExpr:
         dtype: PsType
         match cast_expr.dtype:
             case DynamicType.NUMERIC_TYPE:
@@ -472,7 +472,19 @@ class FreezeExpressions:
             case other if isinstance(other, PsType):
                 dtype = other
 
-        return PsCast(dtype, self.visit_expr(cast_expr.expr))
+        arg = self.visit_expr(cast_expr.expr)
+        if (
+            isinstance(arg, PsConstantExpr)
+            and arg.constant.dtype is None
+            and isinstance(dtype, PsNumericType)
+        ):
+            # As of now, the typifier can not infer the type of a bare constant.
+            # However, untyped constants may not appear in ASTs from which
+            # kernel functions are generated. Therefore, we annotate constants
+            # instead of casting them.
+            return PsConstantExpr(arg.constant.interpret_as(dtype))
+        else:
+            return PsCast(dtype, arg)
 
     def map_Relational(self, rel: sympy.core.relational.Relational) -> PsRel:
         arg1, arg2 = [self.visit_expr(arg) for arg in rel.args]
diff --git a/src/pystencils/backend/kernelcreation/typification.py b/src/pystencils/backend/kernelcreation/typification.py
index fc085e2be99f61204cde92438811a3b4e41c8bf7..ce2d24f985cc91fd3f2e25abcb67220c991b358e 100644
--- a/src/pystencils/backend/kernelcreation/typification.py
+++ b/src/pystencils/backend/kernelcreation/typification.py
@@ -594,7 +594,14 @@ class Typifier:
                     tc.apply_dtype(arr_type, expr)
 
             case PsCast(dtype, arg):
-                self.visit_expr(arg, TypeContext())
+                arg_tc = TypeContext()
+                self.visit_expr(arg, arg_tc)
+
+                if arg_tc.target_type is None:
+                    raise TypificationError(
+                        f"Unable to determine type of argument to Cast: {arg}"
+                    )
+
                 tc.apply_dtype(dtype, expr)
 
             case _: