Abstract: The issue of tool path generation has so far been approached from points of automatic programming system on typified by APT. In the automatic programming system, however, patterns of workpieces should be recognized by operators, and if the workpieces are of complicated shapes, it should require much skill and time. Studies have been conducted in recent years to generate tool paths by building up in advance solid models in a computer, and modifying the models for a particular problem everytime it needs to be solved. According to this invention method, a required shape and an environmental model including a workpiece are modeled in three-dimensions by using CSG models, and are offset in a normal direction of the surface in correspondence to the tool radius to convert the tool into a line tool so that the problem is replaced with a graphic problem viewed from the tool axis direction.