Abstract <p>Experience in oil and gas field development shows that, although the solution to field development problems involving elastic deformation of rocks and compression of the fluids contained therein has been studied in sufficient detail to date, recently field development problems have also begun to be studied based on the fact that the rocks comprising them, especially those located at great depths, can be subject to deformation with inelastic characteristics of a rheological nature. As a continuation of this work, this article develops numerical schemes for solving the problem of gas inflow to a well system in a relaxation-deformable gas reservoir, presenting the conditions for their stability and the feasibility of their implementation. The resulting schemes allow for the necessary assessments to be made for the purpose of reliable control over the development of deep-seated gas fields during their operation with a well system under conditions of relaxation deformation of rocks.</p>