Abstract <p>This article presents a numerical simulation of a Stefan problem to study the thermal impact of a gas well on the permafrost. A numerical investigation of a two-phase Stefan problem was conducted, accounting for phase transitions in the pore space of rocks and their effect on the thermal interaction between a gas well and the cryolithozone in a two-dimensional formulation. The two-phase Stefan problem was solved using the finite element method (FEM), with coupling through a boundary condition at the well contact. The thermal state of the well, described by steady-state continuity and heat transfer equations, was modeled using the Finite Difference Method (FDM). The results provide data on the dynamics of the thaw zone and temperature fields, which are crucial for assessing geotechnical risks.</p>