Control of robotic surface finishing processes such as deburring, grinding, chamfering, and polishing is considered in this paper. A complete dynamic model that describes the dynamic behavior of the robot for surface finishing tasks is developed. A complete surface finishing task is divided into three phases (free motion phase, transition phase, and constrained motion phase) depending on the location of the robot end-effector with respect to the constraint surface. Stable control algorithms are developed for each phase. Emphasis is given to the transition phase and constrained motion phase, where surface finishing takes place. An experimental platform for performing robotic surface finishing operations is developed. The robotic surface finishing system consists of a planar robot with a force sensor and a deburring tool on its end-effector, and a fixture to hold the constraint surface. Extensive experiments based on the proposed control design were conducted for both surface following and surface finishing. Results of surface following and surface finishing experiments are shown and discussed.