Preheat a skillet or griddle over medium heat until hot.
Lightly butter one side of each slice of rye bread; buttered side will contact the pan.
Spread about 1 tablespoon Russian dressing on the unbuttered side of four bread slices.
Layer 2 slices Swiss cheese on each dressed slice to create a melting barrier.
Pile 3–4 ounces of thinly sliced corned beef over the cheese, pressing gently.
Evenly distribute about 3–4 tablespoons sauerkraut atop the beef; squeeze excess liquid first.
Top sauerkraut with another slice of Swiss cheese, then close sandwich with remaining bread (buttered side out).
Place sandwiches butter-side down on the hot skillet; press gently with a spatula or panini press.
Grill 3–4 minutes per side until bread is golden-brown and cheese is melted, flipping carefully.
Remove from skillet, let rest 1 minute, optionally slice in half, and serve immediately.