Despite the fact that worm gears have been known for millennia, they are still used and they are constantly improved and developed. The goal is to obtain a gear that is not wearing out under the assumed operating conditions. That is why such an important issue is the ability to make worms with a defined outline as well as with a certain accuracy. This directly affects the durability of the worm gear. Comparing worm gears with concave-convex surfaces with conventional cooperation surfaces worm gears, they are characterized by: more favorable change in the distribution of Hertz pressure, change in the course of the contact line between the cooperating surfaces and an increase in the thickness of the worm wheel tooth at the base. In this way, improved power transmission and lubrication properties can be expected, what consequently results in less energy loss and less wear. The article presents the method of forming helical surfaces with a circular concave axial profile by the point method and the developed code generation program for controlling a universal multi-axis CNC machine tool.