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Finite element method (FEM) is the effective numerical method for approximate solution of tasks, mathematical formulation which is reduced to a system of differential equations, boundary and initial conditions (the so called boundary value problems). These problems particularly include the challenges of material plastic deformation. The method is widely used in other engineering applications of deformed solid body mechanics, as well as for a solution to problems of electrodynamics, heat transfer and related problems, where different physical phenomena act jointly.