Propagation of shock waves in layered anisotropic tectonic media is associated with their fronts transformation, scattering, bifurcation and focussing. To investigate these phenomena, a technique based on joint usage of ray theory and theory of stereomechanical impact is elaborated. It is used for computer simulation of dynamical interaction of shock waves with curvilinear interfaces between anisotropic elastic media. Issues are considered which are related to the shock waves fronts surfaces bifurcations and generation of caustics connected with stress concentration and formation of zones where the stresses tend to infinity. ©2000 American Institute of Physics.