This paper presents the mathematical model of the gas extraction from a reservoir initially saturated with methane and its hydrate, under conditions of negative (below 0 degrees C) initial temperature of the reservoir. The algorithm is proposed and the numerical scheme is constructed which makes it possible to find the main parameters of the nonisothermal filtration flow in a hydrate-saturated reservoir, taking into account the hydrate decomposition to gas and ice. The analysis of the influences of the mass flow rate of gas extraction, the porous medium permeability, the initial reservoir temperature, and the initial hydrate saturation on the regime and rate of the gas hydrate decomposition was carried out. (C) 2017 Elsevier Ltd. All rights reserved.