Presents an investigation of jerk continuity in milling operations for the sculptured surface of parts. It has long been realized that chattering of machine tools during machining operations can cause detrimental effects on the quality of machined parts as well as on the cutting tool's life. One of the major reasons causing chattering is known to be the rough transition of cutter acceleration changes during machining of different part surfaces. The problem becomes serious when machining sculptured surfaces of parts. In this work, an effective computer aided sculptured surface design technique is proposed. The ultimate goal is to achieve a smooth and near chattering-free machining for producing precision parts. The proposed surface design scheme models part's sculptured surfaces in such a way that it warrants a smooth jerk transition at the boundaries of common surface patches on the part. This results in a drastic reduction of large step changes of cutter accelerations during machining operations which will in turn eliminate a good portion of chattering effects. Three theorems concerning the necessary jerk continuity conditions for surface patches connections are developed and their proofs are presented. Examples of an airfoil and a concept car model are implemented using the proposed modeling approach to demonstrate its effectiveness.