The paper presents the formalism of the parametric integral equation system (PIES) for two-dimensional elastoplastic problems and the algorithm for its numerical solution. The efficiency of the proposed approach lies in the global modeling of a plastic zone, without classic discretization into elements, using surface patches popular in computer graphics. Lagrange polynomials with various number and arrangement of interpolation nodes are used to approximate plastic strains. Three test examples are solved and the obtained results are compared with analytical and numerical solutions. (C) 2016 Elsevier Ltd. All rights reserved.