A finite element analysis of the stress-strain state of a steel ball stamping process from a cylindrical billet was performed under the conditions of a non-isothermal process in an axisymmetric formulation. Three options for stamping a ball from blanks with different height-to-diameter ratios are considered. Distribution of temperature, degree and deformation rate, average stress and stress intensity are given. It has been found that with an increase in the relative workpiece height, the degree of deformation over the ball volume increases. In this case, the temperature value in the ball volume increases. A metal cooldown zone on the periphery of billet ends was revealed. Stress state index assessment at the last stage of stamping made it possible to identify the workpiece dangerous zones from the point of failure. When considering the metal plasticity indicators, this makes it possible to predict the defectiveness of products.