In this paper a method of numerical studies of elastic-plastic bodies with finite deformations is considered. Constitutive relations obtained using the elastic potential in the flow theory. For plasticity condition Huber – Mises hardening condition criterion is applied. Incremental loading procedure is used, where allowing the variation equation is derived from the principle of virtual powers in the current configuration. For the simulation of plastic deformation the surface projection of the stress flow with iterative refinement of the current stress-strain state is applied, based on the introduction of a system of equations in resolving power of additional stresses. The numerical discretization is based on the finite element method. A solution of the test problem of elastic-plastic strain give by a circular bar, the results are compared with data, received by other authors.