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Permafrost plays an important role in global climate change and affects biological, hydrological and human activities in the Arctic. According to the modern understanding, submarine permafrost (SMP) in the Kara Sea shelf can be encountered in the area from the coastline up to the water depth of 120 m, which corresponds to decrease in the sea level during the Last Glacial Maximum about 20,000 years ago. Potential depth of freezing and corresponding SMP thickness could reach 300 to 400 m. A map of SMP distribution of Kara Sea was developed basing on the drilling data and high-resolution seismo-acoustic profiling for SMP identification. The SMP of Kara Sea has a discontinuous character. Data of sea bottom temperature (SBT) from 1900 to 2000 was analyzed, and the rate of SBT increasing was estimated as 0,5 - 2,5 degrees/100 years for the different regions of Kara Sea. 2D computer model of SMP degradation was developed for the numerical calculations. The real rate of the Permafrost degradation under modern thermal conditions is about 2-4 cm. per year. Using the methane content data in the frozen Quaternary sediments it allows us to estimate an additional methane flow into sea water. This study is supported by RSF, grant №16-17-102. Methane content in frozen Quaternary sediments is studied in framework of RFFI grant № 16-05-00612.