pressure, deformation, ideal plasticity, group analysis, symmetries of differential equations, exact decisions, homotopy.

The hyperbolic system of the equations of two-dimensional ideal plasticity with the Tresсa-Saint-Venant-Mises fluidity condition is considered. The technique of decisions reproduction for reception of new decisions and their characteristics is used. Homotopy of the decisions of the considered system which allows to receive the new classes of analytical decisions is constructed. The mechanical sense of received decisions is discussed.