A model of the Antarctic ice sheet has been used to simulate the ice sheet in warmer climates, in order to investigate what kind of ice sheet geometries one canreasonably expect under what kind of climatic conditions and to find out which physical mechanisms may be involved to explain them. The results of theseexperiments reveal the large stability of, in particular, the East Antarctic ice sheet. It would require a temperature rise of between 17 and 20K above presentlevels to remove this ice sheet from the subglacial basins in the interior of the continent and of 25K to melt the Antarctic ice sheet completely down. For atemperature rise below 5K, the model actually predicts a larger Antarctic ice sheet than today as a result of increased snowfall, whereas the West Antarctic icesheet was found not to survive temperatures more than 8-10K above present values. Furthermore, basal temperature conditions in these experiments point tothe problems involved to raise the base to the pressure melting point over the large areas necessary to consider the possibility of sliding instability. Theseresults bear on a lively debate regarding the Late Cenozoic glacial history of Antarctica. In particular, based on these findings it appears difficult to reconcile ahighly variable East Antarctic ice sheet up to the Pliocene with the modest warmings recorded in, for instance, the deep sea records for the Late Neogene.