Most subsea permafrost in the Arctic Ocean shelf regions is relict terrestrial permafrost that was inundated by sea water by rising sea levels after the last glacial period. Permafrost usually degrades offshore under the influence of sea-bottom temperatures, salt infiltration and a wide range of near-shore coastal processes. Subsea permafrost instability has important potential implications due to the release of methane to the atmosphere and by increasing coastal erosion rates. Our objectives are to employ meso-scale numerical calculations (from meter to kilometer, 1000s of years) in connection with borehole data from the Laptev Sea to model the transition of permafrost from onshore to offshore conditions. The goal is to identify key processes driving permafrost degradation in the near-shore zone of the shelf. The heat transfer equation is solved numerically taking into account freeze-thaw processes in a three-phase heat capacity / conductivity model. Sediment composition and initial temperature profiles are derived from field and laboratory analysis of the borehole data. Our approach neglects some processes such as solute diffusion, but includes the effect of pore water salinity on phase state and thermal properties. Measured temperature profiles are compared to the modeled subsea soil temperature evolution over the course of the 2500 year transgression of the farthest offshore borehole in the transect. The degradation of the ice-bearing permafrost table or thaw depth is of special interest due to its direct relation to sediment stability and as the most readily discernible feature in the field observations. Temperature profiles generally agree well with model calculations reproducing the almost isothermal permafrost profiles currently observed, but show more variation potentially partially caused by drilling disturbances. The thaw depth is mainly driven by salt contamination and infiltration into deeper pore water with time. Complicating near-shore processes discussed include the occurrence of bottom-fast sea ice and marine sedimentation rates.