The multiple processes which control motion at the bed of glaciers are too heterogeneous to be modeled directly, but a simple stick-slip slider-block model of a glacier bed allows a statistical mechanical treatment of the physics beneath thin and shallow sloped glaciers. The technique may reconcile apparently contradictory field observations of the relationship between glacier sliding and basal water pressure. Simulations also predict hysteresis in the relationship between water pressure and basal velocities. ¿ American Geophysical Union 1996