A mathematical model developed to calculate the force impact on a punch during high-speed impact extrusion of axisymmetric stepped rod tools (punches, pushers, cutters, etc.) is described in the article. The model is based on a twostage transformation, which is implemented according to the scheme “rectangle – square”, “square – circle”. At the same time, the transformation from square to circle is implemented under the condition of equality of cross-sectional areas, which allows keeping practically unchanged the kinematically possible field of slip lines, including velocity and acceleration hodographs during the transformation from plane to axisymmetric deformation. The first transformation in the developed model is accomplished by transforming (adapting) the previously obtained calculation equations for forming a rectangular workpiece into equations for analyzing the force regime during extrusion of a rod tool with a square cross-section at all stages. During the second transformation the obtained equations for the analysis of the force mode of the punch operation at flat deformation of a square workpiece from the condition of equality of squares are adapted for the analysis of axisymmetric deformation on the basis of using the relations  D_i(d_i) = 1.128A_i(a_i), A_i(a_i) = 0.886D_i(d_i), in which D_i(d_i) – are the required diameters of circular sections of axisymmetric workpiece which are determined by the known values of sides A_i(a_i) of square sections of the workpiece formed under conditions of flat deformation. The proposed scheme for calculating the power parameters of the highspeed impact extrusion process makes it possible to quickly calculate the power mode of formation for any rod step tool with an axisymmetric (round) shape of the transverse steps, using the classical upper estimation method. Taking into account the correct assumptions, this method is effectively used only for analyzing the high-speed impact deformation of flat stepped rod products. Using the proposed technology methodology, in production conditions, it is possible to quickly recalculate the force mode of shaping from flat to axisymmetric deformation and, on this basis, select the equipment (stamping or crank presses, stamping hammers, etc.) necessary for the implementation of the tool manufacturing process.