A new thermomechanical three-dimensional model designed to simulate the evolution of the Antarctic ice sheet over long time periods is presented. This model incorporates the various types of ice flow found in Antarctica: relatively slow inland ice flow that is essentially due to ice deformation, fast ice flow in the regions with ice streams, and ice shelf flow. By coupling these three types of flow, it is possible to predict grounding line migration. Simulations covering four glacial-interglacial cycles have been conducted by forcing this model with a temperature record from Vostok and a sea level record from marine cores. Our findings indicate that grounding line migration induced by sea level changes is the primary factor governing the evolution of the Antarctic ice volume. On the other hand, the altitude of the ice sheet surface at Vostok is driven by accumulation rate variations. The amplitude of the altitude change does not exceed 150 m and is very similar for all the sites located on the Antarctic Plateau. ¿ 2001 American Geophysical Union