On one sheet pan arrange the corned beef into 4 sections. Top with cheese and then sauerkraut. Butter one side of each slice of rye bread and place the butter side up on the other sheet pan.
Place both in the oven with the bread closer to the element. Bake until bread is toasted and the cheese has melted. Remove from the oven. Spread the Russian dressing over the non-buttered sides of the bread and top with corned beef and cheese.