Geological data indicate that global mean sea level has fluctuated on 103 to 106 yr time scales during the last ∼25 million years, at times reaching 20 m or more above modern. If correct, this implies substantial variations in the size of the East Antarctic Ice Sheet (EAIS). However, most climate and ice sheet models have not been able to simulate significant EAIS retreat from continental size, given that atmospheric CO2 levels were relatively low throughout this period. Here, we use a continental ice sheet model to show that mechanisms based on recent observations and analysis have the potential to resolve this model-data conflict. In response to atmospheric and ocean temperatures typical of past warm periods, floating ice shelves may be drastically reduced or removed completely by increased oceanic melting, and by hydrofracturing due to surface melt draining into crevasses. Ice at deep grounding lines may be weakened by hydrofracturing and reduced buttressing, and may fail structurally if stresses exceed the ice yield strength, producing rapid retreat. Incorporating these mechanisms in our ice-sheet model accelerates the expected collapse of the West Antarctic Ice Sheet to decadal time scales, and also causes retreat into major East Antarctic subglacial basins, producing ∼17 m global sea-level rise within a few thousand years. The mechanisms are highly parameterized and should be tested by further process studies. But if accurate, they offer one explanation for past sea-level high stands, and suggest that Antarctica may be more vulnerable to warm climates than in most previous studies.