<p>In this paper, a new method of the cogging process of a forging (type: shaft) consisting in the application of the multi-stage process composed of a preparatory shaping on three different kinds of convex anvils, and also in a primary forging on the flat anvils and the asymmetrical V-shaped ones, is presented. The new, implemented method of forging was subjected to tests in the aspect of the formation of conditions favourable for the location of the maximum values of effective strain in the particular zones of the forging being deformed whereas simultaneously marked by the absence of tensile stresses. That renders it possible to develop a scientific foundation for the development of the rational technology of the cogging process. The effective geometrical parameters of new convex anvils were determined, and the efficiency of different applied technological parameter was analysed, in the aspect of the intensity of the re-forging of the particular zones of an ingot. The investigations were complemented by prognosing the formation of ductile fractures in the course of forging with the application of the Normalized Cockcroft and Latham criterion. The analysis of the spatial strain state and stress was conducted with the application of the finite element method and of the DEFORM-3D software. The comparison between theoretical outcomes, and the outcomes of experiments, within the scope of the investigation indicates a good level of their commensurateness.</p>