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Gas hydrate stability zone (GHSZ) exists in wide areas of the Barents Sea shelf. It is known that the main factors limiting the GHSZ thickness are temperature and pressure, so its value should be changed in the course of climate change, sea-level fluctuations and the formation and degradation of cover glaciation. Investigation of changes in permafrost and GHSZ thickness is carried out by means of mathematical simulation. To set the upper boundary conditions it was created a model of changing paleogeographical conditions, for lower - the geological model. Numerical simulation based on the solution enthalpy formulation of the thermal conductivity equation Stefan and varying parameters of the models to assess their impact on the results of the calculations. Modeling the evolution of permafrost and thickness GHSZ conducted for the area of Shtokman gas and condensate field (central part of the Barents Sea) and the Bear Island area (western part of the shelf). The modeling results showed that the thickness of permafrost in the Shtokman field did not exceed 250-500 m, whereas in the western part of the Barents Sea shelf it reached 300-600 m. In the central part of the shelf in highs of glaciations GHSZ reach up to 1400 m and in the western part of the shelf - 1600 m.