Intended use of the small parameter method in CAE systems based on the following assumptions. It may be that the zero approximation is used as the initial distribution of some vector function shows poor convergence. We can expect that convergence can he improved by using as the initial distribution of the solution obtained by the method of small parameter, taking into account the first approximation. It may be effective for a wide class of nonlinear problems such as problems of heterogeneous plasticity theory. The heterogeneity of the material characterized by the dependence of the yield strength of the coordinate points of the body. The present work is devoted to the problem of elastoplastic torsion of heterogeneous hollow rod with a circular cross section. The outer contour of cross section is covered wholly with plastic zone. The stress state in the first approximation is defined by using of the small parameter method.