In the work with the use of methods of mathematical modeling, the processes of realization of intense plastic deformation in samples from light structural alloys are studied. The main feature of the study is the need to create a mathematical model that adequately describes the nonlinear elastic-plastic behavior of light alloys during pressing. Using the results of a numerical experiment, it is necessary to evaluate the possibilities of various compression schemes to achieve the maximum accumulation of plastic deformations in the processed samples. The accumulation of plastic deformations in bulk samples contributes to a change in the internal structure of materials and, as a consequence, to a change in their physico-mechanical properties. Therefore, the created prognostic mathematical model allows to design an optimal tooling of molds for the processing of light alloys by intense plastic deformation to change the structural and mechanical properties of the materials being studied. Mathematical modeling simplifies the design work and saves a lot of resources.