To successfully combat such gas-dynamic phenomena as sudden releases of coal (rock) and gas or rock bumps, it is necessary to have a clear understanding of the mechanism of destruction of a solid body. To study such a phenomenon in mines is rather labor-intensive for known reasons, but to achieve effective results in this area it is necessary to know more deeply at least the simplest mechanism of destruction of coal (rock) samples during their compression in the press, because the nature of the destruction of samples and massif are the same. Previously, on the basis of experiments on testing coal specimens on the press the fact of specimen destruction by plastic waves was established and the experimental method of determining the velocity of plastic waves V fl during the destruction of specimens was proposed. The authors propose the hypothesis of pulsation of an elastic-plastic wave during its propagation and the generation of a running plastic wave.