Preheat the oven to 350 degrees F (175 degrees C).
Place the green beans and corn into a 2 quart casserole dish, and spread evenly. In a medium bowl, stir together the sour cream and cream of mushroom soup. Spread on top of the corn and beans. Sprinkle shredded cheese over the soup. Stir together the melted butter and cracker crumbs; sprinkle over the top.
Bake for 15 to 20 minutes in the preheated oven, until the cheese is melted and everything is heated through.