Current models describing past configurations of the East Antarctic ice sheet are poorly constrained by observations. Exposure dating of bedrock surfaces using in situ–produced cosmogenic nuclides provides an ideal tool for directly constraining former changes in ice sheet elevation. We present cosmogenic radionuclide 10Be and 26Al measurements in bedrock surfaces and glacially transported cobbles in the Grove Mountains, a group of nunataks within the slow-flowing interior ice sheet dome, hundreds of kilometers from the coastal ice margin and from ice streams. Samples were collected in vertical transects over 500 m of relief. Minimum bedrock and erratic exposure ages show a trend of increasing age with height above the ice sheet, spanning a period from 0.3 to 4.0 Ma and 50–900 ka, respectively. No evidence was found for thicker ice at the Last Glacial Maximum compared to modern ice thickness. The older bedrock exposure ages of 2.5–4.0 Ma require steady-state erosion rates of <0.1 mm k.y.−1. The measured two-isotope bedrock exposure ages are successfully modeled when changes in surface elevation of the ice sheet are described by a combination of linear long-term ice surface lowering and shorter term high-frequency glacial-interglacial oscillations. The best-fit model requires a long-term thinning rate of 50 m m.y.−1 and an elevation change of 100 m over a 100 k.y. glacial cycle.