The ability of models to elucidate climate and ice sheet dynamics at the Eocene-Oligocene climate transition (34 Ma) is limited by a reliance on present-day topography as a boundary condition. We present a reconstruction of the Antarctic palaeotopography at the E-O boundary that restores sediment eroded from the continent. Estimates of sediment volume surrounding Antarctica constrain our restoration. Using data from coring and seismic imaging and allowing for a moderate biogenic fraction, weathering reactions and sediment porosity, a source volume of 5-13 million cubic km is thought to have been removed from an area of ca. 13 million square km. Changes to the East Antarctic landscape by local, regional and continental-scale ice have been estimated using an ice sheet and erosion model. Material is restored in response to basal conditions under a range of modelled ice-sheet configurations. These models can restore 3-4 million cubic km to East Antarctica. In West Antarctica, factors including the variable position of the grounding line make it impractical to use quantitative erosion models. Here we link geological evidence for known or suspected remnants of Eocene topography with our understanding of processes and patterns of erosion and deposition to drive construction of potential surfaces. There are several options for geologically reasonable surfaces that imply 5-10 million cubic km of eroded volume. The uncertainty in eroded volume is muted by the transformation to palaeo-elevation because isostatic compensation generally limits the change in average regional elevation to 15-20% of the thickness eroded.