Using the finite element method, the analysis of the stress-strain state of the process of stamping a steel ball from a cylindrical billet was performed. The problem was solved under the conditions of a nonisothermal process in an axisymmetric formulation. Three variants of stamping the same ball from billets with different height-to-diameter ratios are considered. The distributions of the following parameters are given: temperature, strain and strain rate, average stress and stress intensity. It has been established that with an increase in the relative height of the workpiece, the level of the degree of deformation in the volume of the ball increases. At the same time the temperature value over the volume of the ball increases., a zone of metal cooling was revealed at the periphery of the ends of the workpiece. The assessment of the stress state index at the last stage of stamping made it possible to identify the dangerous zones of the workpiece from the point of failure. When taking into account the indicators of metal ductility, this allows us to predict the appearance of product defects.