Cauchy problem solution for a hyperbolic system of the homogeneous 2-dimensional quasilinear equations

The method of solving the boundary-value problems for hyperbolic system of the homogeneous quasilinear equations of two independent variables with the help of conservation laws is presented. This method is applied to basic boundary problems for the system of two-dimensional plasticity equations under Sent-Venan-Mises yield criterion, as well for the system under Coulomb's criterion.