In order to detect potential problems of a cutter path, geometric verification of the NC milling result is necessary prior to actual machining. Result shape of the workpiece can be computed by subtracting the swept volume of a cutter moving along the path from a solid model representing the stock shape. In this paper, the authors propose an acceleration method of the subtracting operation using the hidden surface elimination mechanism of the 3 dimensional graphics hardware. Before the operation, component surfaces of the cutter swept volume must be tessellated. Computation time of the proposed method is proportional to the total number of polygons approximating the component surfaces. Some portions of the surfaces do not contribute the result shape of the workpiece. Our algorithm reduces the polygons by properly excluding such surface portions from the tessellation. An experimental program is implemented and computations of some sculptured surface milling results are demonstrated.