On the basis of radial-axial rolling of ring billets, resource-saving technologies for metal forming have been created. Determining the rational parameters of this process is the actual scientific and technical task at development of new profiles. The method of three-dimensional finite element modeling is the most effective tool for improving the technological conditions of ring rolling process. However, as practice has shown, the finite element modeling method requires adaptation to each process of metal forming. This is the subject of the present work. The expediency of using dependency for calculating the metal flow stress for finite-element modeling of ring-rolling processes is substantiated. This dependence was developed on the basis of a theory that takes into account the chemical composition of structural carbon steel, its temperature, strain rate, accumulated deformation, and also the processes of dynamic transformation of the metal structure during hot rolling. A computer program for automated determination of dependency parameters has been developed. The analysis of the accuracy of the obtained dependence was performed in relation to the experimental data. In the course of these calculations, the method of automated determination of the metal flow stress was used by spline interpolation of the experimental data included in the computer database of digital information for a particular steel grade. The average relative error of calculated values of the metal flow stress was 8 % relative to the experimental ones. An improved method is proposed for calculating the parameters of ring billets rolling and reaching the required growth rate of the ring diameter implemented in a finite element modeling system, which is similar to the way the control system of the ring-rolling mill works in solving the same problem (reaching the required growth rate of the ring diameter) when implemented appropriate rolling in practice. When calculating the size of the compression, the iterative process and the method of half division were used. The average deviations of calculated values of the parameters of ring billets rolling from the experimental did not exceed 12.4 %, which makes it possible to apply the proposed approach to study the patterns of the rings rolling process and to improve the rolling technology.