Asymmetric upsetting is the profiling operation at the metal forming. Using of this operation reduces metal consumption at the metal forming and increases the indicators of physical and mechanical properties of the materials. Also asymmetric upsetting increases the indicators of precision of metal products. Thus theoretical analysis of metal shape change at the asymmetric upsetting is an actual task. The features of the metal flow during asymmetric upsetting of cylindrical billet by convex radial dies are theoretically considered in the article. Preliminary computer modeling was carried out with the determination of the vectors of displacement of material particles of the workpiece metal and characteristic sections of the deformation zone. A design scheme for the process of asymmetric upsetting of the workpiece with radial dies has been developed and the basic geometric ratios for characterization of the strain state and forming of the workpiece after asymmetric upsetting have been determined. The presence of a neutral material flow surface is established. Results of this article improve the accuracy of assessing the unevenness of deformation and the metal flow parameters at the asymmetric upsetting. Also results of theoretical analysis, obtained in the article, allow you to more accurately choose the instrument configuration, the temperature and the deformation modes at the design of stamping processes using asymmetric upsetting of cylindrical billets by convex radial dies. Accounting for the effect of displacement of the neutral cross section of the deformation zone allows you to control and reduce the ram skewness at the design of stamping processes using asymmetric upsetting of cylindrical billets by convex radial dies.