In this paper the mathematical model of the carbon dioxide injection into a natural reservoir initially saturated with methane and its hydrate was constructed and also the research, using this model, was carried out. Self-similar solutions of this problem in the one-dimensional formulation were built. These solutions explain the distribution of the main parameters in a reservoir. It is shown that there are two possible regimes: the first - the recovery of methane from hydrate can occur without decomposition of CH4 hydrate to gas and water, the second - with decomposition. In the first regime, the replacement of methane in hydrate with carbon dioxide is occurs. In the second regime the decomposition of CH4 hydrate to gas and water with the subsequent formation of hydrate from water and carbon dioxide is occurs. The critical diagrams of the each regime existence were built and analyzed. The influence of the injection pressure of carbon dioxide and the reservoir permeability to the speed of methane recovery from hydrate for the each regime was researched. (C) 2016 Elsevier Ltd. All rights reserved.