An analytical solution to the development of a glacier or ice sheet in a region where the underlying rock rises steadily shows that the ice mass oscillates in size, independefntly of changes in the climate, in response to a feedback in which ice thickness is linked to topography by ice-induced erosion. The rate of vertical movement of the underlying rock uplift and the parameters governing ice erosion, ablation, and precipitation determine the period of oscillation. Two-dimensional numerical simulations show that the tectonic uplift rate is the most important control on the period of oscillation and that the feedback period is likely to be between 10 and 100 kyr. An examination of sediment data from the Deep Sea Drilling Project shows evidence of ice mass oscillations in the Chugach-St. Elias Mountains and in the Himalayas with periods consistent with those produced by the proposed mechanism. Localized changes in glacial extent may not therefore always be the consequence of climate change, and care must be taken in interpreting evidence of glacial advance and retreat.