Pencil-curve machining, which is a single-pass ball-end milling along a concave edge on adie surface, is widely employed in die-surface machining. The cutter-path used for pencil-curve machining, which is the trajectory of the “ball-center point” of a ball-endmill sliding along a concave-edge region on the die surface, is called pencil-curve. Presented in the paper is a pencil-curve tracing algorithm in which “concave-type” sharp edges are computed from a “virtually digitized” model of the tool-envelope surface. The resulting “initial” pencil-cures are then refuted by applying a series of fairing operations. illustrative examples and methods for enhancing accuracy are also presented. The proposed pencil-curve tracing algorithm has been successfully implemented in a commercial CAM system specialized in die-machining and in the CAD/CAM system CATIA.