A new method is presented in which the hob profiles for gear-shaped workpieces having arbitrary profiles can be numerically determined without solving transcendental equations as usual. The proposed method is based on iterating the successive approximation until the boundary contour produced by machining converges to a certain limit depending on the desired machining accuracy. Another method is also described in which the workpiece profile to be generated by using the designed hob can be examined. By using these methods, the design of hobs for gear-shaped workpieces having arbitrary profiles will be accomplished easily and the aspect of the cutting interference during hobbing can be examined without difficulty.