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The objectives of research: The generalized plasticity condition and corresponding constitutive equations characterizing some features of materials behavior under different loading conditions, such as stress state dependence of plastic properties, materials dilatation and others are formulated. An algorithm and program for numerical simulation are developed. The analytical solutions of boundary value problems for notched solids with properties dependent on the type of external forces obtained with the use of rigid-plastic model are compared with the results of numerical simulations on the base of elastic-plastic model.