The Weddell Sea sector of the Antarctic Ice Sheet is hypothesized to have made a significant contribution to sea-level rise since the Last Glacial Maximum. Using a numerical flowline model we investigate the controls on grounding line motion across the eastern Weddell Sea and compare our results with field data relating to past ice extent. Specifically, we investigate the influence of changes in ice temperature, accumulation, sea level, ice shelf basal melt, and ice shelf buttressing on the dynamics of the Foundation Ice Stream. We find that ice shelf basal melt plays an important role in controlling grounding line advance, while a reduction in ice shelf buttressing is found to be necessary for grounding line retreat. There are two stable positions for the grounding line under glacial conditions: at the northern margin of Berkner Island and at the continental shelf break. Global mean sea-level contributions associated with these two scenarios are ~50 mm and ~130 mm, respectively. Comparing model results with field evidence from the Pensacola Mountains and the Shackleton Range, we find it unlikely that ice was grounded at the continental shelf break for a prolonged period during the last glacial cycle. However, we cannot rule out a brief advance to this position or a scenario in which the grounding line retreated behind present during deglaciation and has since re-advanced. Better constraints on past ice sheet and ice shelf geometry, ocean temperature, and ocean circulation are needed to reconstruct more robustly past behavior of the Foundation Ice Stream.