We investigate the response of relict Arctic submarine permafrost and gas hydrate deposits to warming and make predictions of methane gas flux to the water column using a 2-D multiphase fluid flow model. Exposure of the Arctic shelf during the last glacial cycle formed a thick layer of permafrost, protecting hydrate deposits below. However, talik formation below paleo-river channels creates permeable pathways for gas migration from depth. An estimate of the maximum gas flux at the present time for conditions at the East Siberian Arctic Seas is 0.2047 kg yr−1 m−2, which produces a methane concentration of 142 nM in the overlying water column, consistent with several field observations. For conditions at the North American Beaufort Sea, the maximum gas flux at the present time is 0.1885 kg yr−1 m−2, which produces a methane concentration of 78 nM in the overlying water column. Shallow sediments are charged with residual methane gas after venting events. Sustained submergence into the future should increase gas venting rate roughly exponentially as sediments continue to warm. Studying permafrost-associated gas hydrate reservoirs will allow us to better understand the Arctic's contribution to the global methane budget and global warming.