We use the Glimmer ice sheet model to simulate periodic surges over the Laurentide Ice Sheet during the Last Glacial Maximum. In contrast to previous studies we use the depth of water at the base of the ice sheet as the switch for these surges. We find that the surges are supported within the model and are quite robust across a very wide range of parameter choices, in contrast to many previous studies where surges only occur for rather specific cases. The robustness of the surges is likely due to the use of water as the switch mechanism for sliding. The statistics of the binge–purge cycles resemble observed Heinrich events. The events have a period of between 10 and 15 thousand years and can produce fluxes of ice from the mouth of Hudson Strait of 0.05 Sv – a maximum flux of 0.06 Sv is possible. The events produce an ice volume of 2.50 × 106 km3, with a range of 4.30 × 106–1.90 × 106 km3 possible. We undertake a suite of sensitivity tests varying the sliding parameter, the water drainage scheme, the sliding versus water depth parameterisation and the resolution, all of which support the ice sheet surges. This suggests that internally triggered ice sheet surges were a robust feature of the Laurentide Ice Sheet and are a possible explanation for the observed Heinrich events.