Contemporary methods of cutting are based on the usage of traditional cutting tools. One of the least studied process of forming workpiece profiles is rotary turning. Despite the comparatively big number of its advantages, which has led to the wide scope of its application since the beginning of the twentieth century, this method has not found extensive research thus far. Existing studies do not allow comprehensive development of a completely new design of rotary cutters. Mathematical simulation of various profiles obtained by rotary turning allows understanding the process of rotary turning of helical surfaces, which, alongside with other complex-shaped surfaces, are the most difficult to obtain, whereas simple-shaped surfaces, viz. Flat, cylindrical, or tapered, contrastingly, are rather easily obtainable. Considering several types of working elements of rotary cutters allows expanding the range of applied cutters and thus simulate the best processing, including processing of helical surfaces. By now, mathematical simulation for machining complex-shaped surfaces with rotary cutters is poorly studied although available mathematical models of methods relating to rotational machining of screw surfaces can allow accelerating the implementation of rotary cutting. The given article discusses mathematical simulation of obtained surface profiles by turning helical surfaces with the flanks of the round-shaped working elements of rotary cutters. Besides, technologically advanced and widely used round disks with a straight-lined and positive-shaped relieving are applied as working elements of rotary cutters. The cutting process is conducted while the removed chips contact with the lateral relieved surfaces of round-shaped working elements of rotary cutters.