It is proposed that ice masses in fast growing orogens oscillate in size, independently of changes in the climate, in response to a feedback in which ice thickness is linked to topography by the erosion caused by the presence of the ice. A one dimensional analytical model implies that the period of oscillation is constant and is determined by the rate of tectonic uplift and the parameters governing ice erosion, ablation and precipitation. Two dimensional numerical experiments show that the tectonic uplift rate is the most important control on the period of oscillation. An examination of sediment data from the Deep Sea Drilling Project shows evidence of ice mass oscillations in the Chugach-St. approximately Elias Mountains and in the Himalayas with period lengths consistent with those produced by the proposed mechanism. Localized changes in glacial extent may not therefore always be the consequence of climate change, and that care must be taken in interpreting evidence of glacial advance and retreat.