Abstract. A two-dimensional model of a passive continental margin was adapted to the simulation of the methane cycle on Siberian continental shelf and slope, attempting to account for the impacts of glacial/interglacial cycles in sea level, alternately exposing the continental shelf to freezing conditions with deep permafrost formation during glacial times, and immersion in the ocean in interglacial times. The model is used to gauge the impact of the glacial cycles, and potential anthropogenic warming in the deep future, on the atmospheric methane emission flux, and the sensitivities of that flux to processes such as permafrost formation and terrestrial organic carbon (Yedoma) deposition. Hydrological forcing drives a freshening and ventilation of pore waters in areas exposed to the atmosphere, which is not quickly reversed by invasion of seawater upon submergence, since there is no analogous saltwater pump. This hydrological pump changes the salinity enough to affect the stability of permafrost and methane hydrates on the shelf. Permafrost formation inhibits bubble transport through the sediment column, by construction in the model. The impact of permafrost on the methane budget is to replace the bubble flux by offshore groundwater flow containing dissolved methane, rather than accumulating methane for catastrophic release when the permafrost seal fails during warming. By far the largest impact of the glacial/interglacial cycles on the atmospheric methane flux is attenuation by dissolution of bubbles in the ocean when sea level is high. Methane emissions are highest during the regression (soil freezing) part of the cycle, rather than during transgression (thawing). The model-predicted methane flux to the atmosphere in response to a warming climate is small, relative to the global methane production rate, because of the ongoing flooding of the continental shelf. A slight increase due to warming could be completely counteracted by sea level rise on geologic time scales, decreasing the efficiency of bubble transit through the water column. The methane cycle on the shelf responds to climate change on a long time constant of thousands of years, because hydrate is excluded thermodynamically from the permafrost zone by water limitation, leaving the hydrate stability zone at least 300 m below the sediment surface.