Paleo-ice sheet reconstructions are complicated by large uncertainties, particularly since it is usually only possible to infer thickness from indirect means such as the response of glacial isostatic adjustment (GIA). Recently, there has been increased attention to refining the chronology of ice sheet margins of paleo-ice sheets, and changes in relative sea level in formerly glaciated regions. Using this information, it is possible to infer the configuration of the ice sheets through time. Using the program ICESHEET (Gowan et al 2016), we reconstruct past ice sheets using a simple, though glaciologically plausible ice sheet model. The ice sheet volume is reconstructed by adjusting the basal shear stress at discrete time intervals in the region of interest until the modelled sea level is consistent with the sea level indicators. We demonstrate this technique by applying it to the Innuitian Ice Sheet. We also show the utility of the models for use in paleo-geographic reconstructions, as well as usage in paleo-climate simulations.