Today the issue of gas production technology from existing gas hydrate deposits discovered on the shelf of the World Ocean and in permafrost areas is still very significant since the methane reserves in the free state are significantly inferior to its reserves in the form of its gas hydrates. One of the tasks for possible gas production from a hydrate-containing porous medium is to study the process of gas hydrate decomposition under thermal and depression effects since they are most commonly used ones. It is necessary to conduct a theoretical study including the development of a mathematical mode and its algorithmization, the creation of a computational program and the conduct of numerical experiments. The paper presents one-dimensional axisymmetric problem of heating and/or pressure reduction at the bottom of a well passing through the entire thickness of a porous formation when its pores are initially filled with methane and its hydrate. The utilized mathematical model includes the continuity equations for methane, its hydrate and water; the equation of the gas phase motion in a porous medium as the Darcy filtration law; the state equation of methane and water, the energy conservation equation considering the Joule–Thomson effects and adiabatic cooling for gas, the latent heat of the “gas hydrate methane + water” phase transition. A numerical implementation of the proposed mathematical model and a numerical study of the thermal and/or depression impact on the studied hydrate-bearing deposit are carried out. The results of calculations show that the size of a zone containing only the gas hydrate decomposition products (gas and water) slightly increases with a smaller length of a porous layer. They also show that the thermal effect (increasing the temperature at the bottomhole of production well) on the hydrate-saturated reservoir simultaneously with the depression effect is not efficient enough due to the intensive flow of cold gas (with a temperature equal to the initial temperature of the reservoir) from the hydrate-containing deposit to the well.