During the middle and late Eocene (∼48-34 Myr ago), the Earth's climate cooled1,2 and an ice sheet built up on Antarctica. The stepwise expansion of ice on Antarctica3,4induced crustal deformation and gravitational perturbations around the continent. Close to the ice sheet, sea level rose5,6despite an overall reduction in the mass of the ocean caused by the transfer of water to the ice sheet. Here we identify the crustal response to ice-sheet growth by forcing a glacial-hydro isostatic adjustment model7 with an Antarctic ice-sheet model. We find that the shelf areas around East Antarctica first shoaled as upper mantle material upwelled and a peripheral forebulge developed. The inner shelf subsequently subsided as lithosphere flexure extended outwards from the ice-sheet margins. Consequently the coasts experienced a progressive relative sea-level rise. Our analysis of sediment cores from the vicinity of the Antarctic ice sheet are in agreement with the spatial patterns of relative sea-level change indicated by our simulations. Our results are consistent with the suggestion8 that near-field processes such as local sea-level change influence the equilibrium state obtained by an icesheet grounding line.