Abstract The surface of wormwheel toothing is determined as the envelope of the action surface of the tool, which a special wormwheel hob or a modular hob. The tool and the machined wormwheel form a worm–wormwheel technological gear in the machining process. In the gear, the rotary motion of the worm can be converted into translational motion, thus simplifying the problem solution algorithm. Moreover, the numerical method enables the determination of the wormwheel tooth surface without having to solve the envelope condition.