Stagnation of the terminal region of a glacier occurs in response to sufficiently large and rapid climatic warming, so the presence of stagnation deposits provides quantitative information on the climate change that forced retreat. Here we use a simple flow-line glacier model to investigate the relationship between stagnation, climate forcing and aspects of the glacier bed. For climatic warming greater than the threshold to cause stagnation, larger or faster warming events cause longer regions of a glacier to stagnate. Smaller or slower warming episodes, below the threshold for stagnation, cause retreat while active flow persists along the entire glacier length. The threshold for stagnation depends not only on the climatic forcing but also on many other aspects of the glacier, with stagnation favored by factors including a lower mean bed slope with greater roughness. Quantitative determination of the climatic forcing consistent with the occurrence or absence of stagnation deposits requires that these site-specific characteristics be incorporated in modeling.