Arctic sources of greenhouse gas associated with permafrost degradation constitute a large uncertainty in existing climate models. Greenhouse gas release from the Arctic subsurface is mediated by numerous interconnected physical processes; one facet of these is the interplay between surface deformation and melting of subsurface ice. First, we construct analytic solutions describing fluid drainage and soil subsidence subsequent to thawing of a 1‐D permafrost column. These solutions lead to formulas giving the total amount of subsidence as well as the time over which subsidence occurs. We give an example application of the analytic model to peat plateau degradation in the Canadian Hudson Bay Lowland and show that the degree of subsidence predicted from our model is consistent with recorded subsidence of peat in western Norway that was drained for cultivation purposes. Second, we numerically model an initially frozen, fluid‐saturated, 2‐D soil matrix with a thaw zone advancing from the surface downward. With the surface temperature fixed at 5°C, a thaw front propagates to ∼10 m depth within 20 years, and due primarily to drainage of fluid from the pore space, a region of soil depressed by ∼3 m forms above an initially ice‐rich subsurface zone. Soil underlying this depressed zone may have its permeability reduced by between 1 and 2 orders of magnitude; this reduction in permeability can act as a negative feedback to thawing.