A retaining ring can be shaped by machining or lapping the bottom surface of the ring to form a shaped profile in the bottom surface. The bottom surface of the retaining ring can include flat, sloped and curved portions. The lapping can be performed using a machine that dedicated for use in lapping the bottom surface of retaining rings. During the lapping the ring can be permitted to rotate freely about an axis of the ring. The bottom surface of the retaining ring can have curved or flat portions.