In the paper, the results of numerical solution to the inverse problem for a system of elasticity for vertically inhomogeneous medium are presented. The center of compression excites the elastic oscillations in medium. This mathematical model of source does not give a decomposition of the elastic system and we need to solve numerically the inverse problem for all system. It is necessary to find the longitudinal velocity vp and the transverse velocity vs in each layer if longitudinal and transverse displacements are known on the surface. The results of reconstructions of velocities for medium typical for Western Siberia are presented. It is shown that satisfactory reconstruction is possible if the inverse problem data with error in 5-40%.