Compound surface modeling is widely used for die cavities and punches. A compound surface is defined in 3-D space by specifying the topological relationship of several anlytic surface elements and a sculptured surface. A constructive solid gemonetry scheme is employed to model the analytic compound surface. the desired compound surface can be accomplished by specifying topological reationship in terms of boolean relations between pimitives and the sculptured surfaces. Additionally, a method is presented for checking and avoiding the tool interference occuued in machining the compound surface. Using this method. the interference of concave, convex, and side region can be checked easily and avoided rpapidly