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In this research paper developed a three-dimensional mathematical model of the process of gas filtration in porous media in the presence of a mass transfer through the boundaries and a numerical algorithm for solving the stated initial-boundary value problem. The developed model is described using a non-linear partial differential equation with appropriate initial and boundary conditions. The proposed mathematical apparatus makes it possible to carry out hydrodynamic calculations, taking into account changes in the main factors affecting the process under consideration: permeability, porosity and thickness of formations, gas recovery coefficient, viscosity, etc. A numerical algorithm has been developed to solve the problem based on difference schemes of the second order of approximation in time and coordinates, which provide the ability to solve practical problems of analyzing and predicting the gas production process under various conditions of impact on the productive reservoir, as well as making decisions on the development of existing and design of new gas fields. Meanwhile, the use of three-dimensional models makes it possible to more accurately describe the processes occurring in reservoir porous media. Therefore, the purpose of this study is to develop a three-dimensional mathematical model of gas filtration in porous media in the presence of a mass transfer through the boundaries, as well as a numerical algorithm for solving the problem. [ABSTRACT FROM AUTHOR]