A method known in the general theory of nonlinear waves is extended to problems dealing with shock-loaded materials obeying elastic-plastic deformation kinetics. As a result a set of approximate independent nonlinear equations belonging to different families of longitudinal characteristics is obtained. It is shown that the interaction of these waves may be described implicitly by a heterogeneous shift of the phase variable in the solution constructed without regard for the interaction. The self-action structure of an incident wave reaching a free surface of a metal plate has been considered on the basis of the equations obtained. This effect is important for the correct interpretation of experimental data.