The purpose of this article is to study the problem of the propagation of waves that result in earthquakes in different geological media: homogeneous, multilayer, gradient, with fractured layer, and karst cavern. The authors pose the problem of analyzing the impact of waves on ground structures: buildings and dams. Numerical solutions of problems of wave propagation in heterogeneous media are obtained. On the basis of the analysis of wave patterns, the types of waves propagated from the focus of the earthquake are qualified. The comparison of the impact of elastic waves on the day surface for the cases of different geological media is done. Synthetic seismograms for these media are obtained. The influence of elastic waves on the stability of ground structures is qualitatively examined. The grid-characteristic method for triangle meshes with the formulation of boundary conditions on interfaces of rock-crack, building-rock, rock-water, and dam-water, as well as free surfaces in an explicit form, is used in this paper. © 2012, Pleiades Publishing, Ltd.