Variability in tidewater outlet glacier behavior under similar external forcing has been attributed to differences in outlet shape (i.e., bed elevation and width), but this dependence has not been investigated in detail. Here we use a numerical ice flow model to show that the dynamics of tidewater outlet glaciers under external forcing are highly sensitive to width and bed topography. Our sensitivity tests indicate that for glaciers with similar discharge, the trunks of wider glaciers and those grounded over deeper basal depressions tend to be closer to flotation, so that less dynamically induced thinning results in rapid, unstable retreat following a perturbation. The lag time between the onset of the perturbation and unstable retreat varies with outlet shape, which may help explain intra-regional variability in tidewater outlet glacier behavior. Further, because the perturbation response is dependent on the thickness relative to flotation, varying the bed topography within the range of observational uncertainty can result in either stable or unstable retreat due to the same perturbation. Thus, extreme care must be taken when interpreting the future behavior of actual glacier systems using numerical ice flow models that are not accompanied by comprehensive sensitivity analyses.