Abstract. In this paper, a porous medium whose core is built from a solid substance is considered. Such a medium can accumulate liquid and gaseous substances absorbing on the surface of the solid body and diffusing within its molecular lattice. The medium forms a so-called solid solution. A change in the values of the thermodynamic parameters of this; medium leads to phase transitions in these substances. Besides, some other associated phenomena may occur. There are given the results of laboratory analyses concerning the relation between the specific volume V of the solid solution formed by the coal with CO2, CH4, N2 dissolved in it and its corfining pressure p. This relation indicates the possibility of the propagation of a rarefaction shock waves in such a medium.A mathematical model of the generation of such waves and its specific applications to describe the initial boundary conditions affected during the experiments presented. The results of these experiments have confirmed the adopted model, particularly those aspects that are concerned with the specific sliced structures of the coal medium with the accumulated CO2 and N2, through which a rarefaction shock wave has passed (Figs. 10a, 10b, lla, and llb). The presented model explains the phenomena of sudden massive rock-and-gas outbursts, occurring in nature, e.g. as a result of disturbing the primary equilibrium of the rocks in the Earth crust which form a solid solution, by underground mining exploitation.