Results of the mathematical modeling of the dynamics of the submarine permafrost and the methane hydrate stability zone in the sediment of the East Siberian Arctic shelf are presented. The thickness of permafrost on the shelf is 175—320 m for the geothermal heat flux 60 mW/m according to the results of experiments. The permafrost modeling indicates to the fact that after the seafloor warming from 1948 to 2012 the permafrost upper boundary deepens for only about 1-20 m. The thawing permafrost dynamics is more sensitive to the magnitude of the heat flux than to the bottom water temperature changes. A possible existence of close and open taliks in the permafrost in the Laptev Sea is shown.

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