After a brief exposition of considerations which push (induce) to construction of relativistic elasticity, a pattern of the theory of deformation of a continuous medium in the framework of the general relativity is given. In the case of elastic medium, the properties of the formation of shocks starting from the infinitesimal discontinuity are established and also remarkable results concerning the propagation discontinuities in a state of strong hydrostatical compression typical of the physics of dense stars. It is discussed the utilization of an elastic pattern identical and its generalization in the frame of electrodynamic relativistic of continuous medium for interpretation of phenomena fit for being registered by the aid of elastic detectors of gravitational waves.