In modern mechanical engineering, electrical discharge machining (EDM) methods are widely used for machining bodies of rotation from difficult-to-machine materials. Those methods ensure sparing cutting and make it possible to machine any electrically conductive material irrespective of its physical and chemical properties, in particular hardness. There is a known method for dimensional machining of bodies of rotation with electric arc using a wire electrode tool that is pulled along in the machining area thus "compensating" for that tool's EDM wear and tear. The machining accuracy is therefore significantly heightened. However, when implementing this method, an effect of splashing the working fluid outside the working area of the machine and a pronounced luminous effect from the burning of the electric arc in the machining area are observed. That worsens the working conditions. In addition, when pulling the wire electrode tool along the convex surface of the electrode holder, the sliding friction arises, which eventually leads to mechanical destruction of the contact point. As a result, a deep kerf is formed on the electrode holder. When the depth of the kerf reaches the diameter of the wire electrode tool, the destruction of the electrode holder by the electric arc begins. Consequently, the durability of the electrode holder in the known method is unsatisfactory. A method of dimensional machining of bodies of rotation with electric arc using a wire electrode tool with the immersion of the machining area in the working fluid has been proposed, which makes it possible to improve the working conditions of the operator by eliminating the effect of fluid splashing and removing the luminous effect of arc burning in the machining area. In addition, it has been proposed to make the electrode holder in the form of a roller that rotates with a guide groove for the wire electrode tool, while the nozzle for creating the transverse hydrodynamic fluid flow has been proposed to be mounted in a separate fixed housing that is adjacent to the electrode holder. This technical solution replaces the sliding friction with the rolling one thus enhancing the durability of the electrode holder. Mathematical models of the process characteristics of the DMA-process (dimensional machining with electric arc) for bodies of rotation using a wire electrode tool with the immersion of the machining area in the working fluid have been obtained that make it possible to control the machining productivity, the specific machining productivity, the specific electric power consumption, and the roughness of the surface machined.