A three-dimensional numerical model of ice flow has been developed to study the areal distribution of mass in an ice sheet of arbitrary shape that is not necessarily in a steady state. The model was applied to the 5900 km2 Barnes Ice Cap, Baffin Island, Northwest Territories, Canada, as a test case, and the results were compared with the present day ice cap. The results were generally consistent with glaciological and glacial geological field evidence. The results suggest that basal sliding may be occurring beneath the southwestern side of the present ice cap. The model has general applicability to several studies involving the question of the speed of ice sheet development and the time/load history of the last major glaciation.