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In arctic and subarctic regions the climate change is leading to the melting of permafrost and there is a vital need to assess the timing and extent of the current process. Numerical simulation of the thermal state of permafrost soils is performed in the conditions of the city of Yakutsk. A 1D Stefan problem is solved using climatic data of the general circulation model GFDL CM2.1. The developed model of permafrost accounts for monthly average air temperature, parameters of snow cover (thickness, density, thermal conductivity), radiation balance of the earth surface, wind speed. On the output, profiles of ground temperature and depths of the permafrost top edge are obtained for moderate and aggressive climate warming scenarios up to the year 2100. [ABSTRACT FROM AUTHOR]