On the longer climatic time scales, changes in the elevation and extent of the Antarctic ice sheet have an important role in modulating global atmospheric andoceanographic processes, and contribute significantly to world-wide sea levels. In this paper, a 3-D time-dependent thermomechanical model for the entire icesheet is presented that is subsequently used to examine the effects of glacial-interglacial shifts in environmental boundary conditions on its geometry. Themodel takes into account a coupled ice shelf, grounding-line dynamics, basal sliding and isostatic bed adjustment and considers the fully coupled velocity andtemperature fields. Ice flow is calculated on a fine mesh (40 km horizontal gridsize and 10 layers in the vertical) for grounded and floating ice and a stresstransition zone in between at the grounding line, where all stress components contribute in the effective stress in the flow law. There is free interactionbetween ice sheet and ice shelf, so that the entire geometry is internally generated. A simulation of the present ice sheet reveals that the model is able to yieldrealistic results. A series of sensitivity experiments are then performed, in which lower temperatures, reduced accumulation rates and lower global sea levelstands are imposed, either singly or in combination. By comparing results of pairs of experiments, the effects of each of these environmental changes can bedetermined. In agreement with glacial-geological evidence, we found the most pronounced changes to show up in the West Antarctic ice sheet configuration.They appear to be essentially controlled by variations in eustatic sea level, whereas typical glacial-interglacial changes in temperature and ice deposition ratestend to balance one another. These findings support the hypothesis that the Antarctic ice sheet basically follows glacial episodes on the northern hemisphereby means of sea-level teleconnections. Grounding occurs more readily in the Weddell sea than in the Ross sea and long time scales appear to be involved: itmay take up to 30-40000 years for these continental shelf areas to become completely grounded after an initial stepwise perturbation in boundary conditions.According to these reconstructions, a steady state Antarctic ice sheet may contribute some 16 m to global sea level lowering at maximum glaciation.