Place squash and water to cover in a medium saucepan. Bring to a boil. Reduce heat; cover and cook 10 minutes. Drain well. Mash squash; drain once again. Set aside.
Sauté onion, celery, and green pepper in butter in a large skillet until vegetables are tender; remove from heat. Stir in squash, cheese, cracker crumbs, eggs, milk, salt, and pepper.
Pour mixture into a 12- x 8- x 2-inch baking dish. Bake, uncovered, at 375° for 30 minutes. Serve immediately.