<p>By mathematical-modeling methods, the authors investigate the process of injection of superheated steam into a gas-hydrate stratum. In constructing a mathematical model, it has been assumed that phase transitions (of condensation of vapor and evaporation of water and of formation and decomposition of methane hydrate) occur in certain finite volumes of a porous medium that are determined in the course of the solution of the problem with the phase saturations, rather than on frontal surfaces. On the basis of numerical solutions, it has been shown that near the boundary of injection of the steam, a complete decomposition of methane hydrate occurs on the frontal surface, in practice. Here, near the boundary of extraction of the gas, the decomposition of methane hydrate occurs in the volume region, which is due to the reduction in the pressure. It has been shown that the increase in both the injection pressure of the steam and its temperature has no substantial effect on the amount of methane hydrate decomposing in the stratum. It has been established that the increase in the permeability of the stratum leads to a greater heating of the stratum and a larger amount of the decomposed gas hydrate.</p>