Traditional models of Glaciol isostasy, derived predominantly for studying the response of the earth to the retreat of Northern Hemisphere ice sheets since the last ICC age, use earth models which assume constant lithospheric thickness. For Antarctica, where the continent below the ice sheet is two separate land masses differing in geological form, the assumption thai a uniform lithosphere can explain isostatic bchavioitr is questionable. Here, a method to calculate the glacio-isostatic adjustment of the continent with a laterally varying lithospheric thickness IS presented. The method is then used in a time-dependent ice-sheet model to model the isostatic response of the continent when the ice sheet passes through a Glaciol/interglacial transition. Various relations bet ween the “crustal thickness” beneath Antarctica, derived from seismic data, and the “lithospheric thickness” estimate used in glacio-isostatic calculations are assumed in a sensitivity study. Using the simplest relationships between crustal and lithospheric thickness, the greatest sensitivity of the ice sheet to the crustal structure of Antarctica is not in the interior but at coastal locations, particularly near the major ice shelves. During periods of ice-sheet advance the grounding-line migration of the shelves varies according to the depression of the earth peripheral to the ice sheet. The peripheral depression depends on the regional elasticity of the lithosphere which is controlled by the lithospheric thickness. Therefore the capacity for the ice sheet to advance varies with the regional thickness of the crust.