A time-dependent numerical model has been developed to study the dynamics of a polar ice stream grounded below sea level. The model was applied to ice stream E, one of the two most active ice streams draining the Ross Sea sector of the West Antarctic ice sheet. The retarding force, or back stress, from the floating Ross Ice Shelf needed to hold the model grounding line in dynamic equilibrium was found to compare closely with retarding force mapped from field data by earlier investigators. This implies that the grounding line of ice stream E is in fact close to dynamic equilibrium, neither advancing nor retreating rapidly, if the ice stream and its catchment area are approximately in mass balance. Sensitivity tests showed that the model ice stream is more sensitive to charges in back stress from the ice shelf than to changes in the accumulation rate. Changes in back stress can be caused by changes in the average thickness of the ice shelf. The model was used to simulate retreat of the ice stream from the edge of the continental shelf in the Ross Sea during the Holocene period of rising sea level. The seafloor was assumed to be isostatically expressed but to remain rigid during retreat. The effect of the assumed retreat history of the Ross Ice Shelf on the computed timing of grounding-line retreat was investigated by considering several alternative ice shelf histories. The results support the conclusion of earlier investigators that the Ross Ice Shelf caused the grounding line to stop retreating near its present position, after extensive retreat during the Holocene. In addition, the timing of retreat of the calving front of the Ross Ice Shelf exerted major influence on the timing of retreat of the ice stream grounding line.