The elevation history of the Tibetan plateau provides direct insight into the tectonic processes associated with continent-continent collisions. Here we present oxygen-isotope-based estimates of the palaeo-altimetry of late Eocene and younger deposits of the Lunpola basin in the centre of the plateau, which indicate that the surface of Tibet has been at an elevation of more than 4 kilometres for at least the past 35 million years. We conclude that crustal, but not mantle, thickening models, combined with plate-kinematic solutions of India-Asia convergence, are compatible with palaeo-elevation estimates across the Tibetan plateau.