In most models of the flow of glaciers on till beds, it has been assumed that till behaves as a viscoplastic fluid, despite contradictory evidence from laboratory studies. In accord with this assumption, displacement profiles measured in subglacial till have been fitted with viscoplastic models by estimating the stress distribution. Here we present a model that illustrates how observed displacement profiles can result from till deformation resisted solely by Coulomb friction. Motion in the till bed is assumed to be driven by brief departures from static equilibrium caused by fluctuations in effective normal stress. These fluctuations result from chains of particles that support intergranular forces that are higher than average and that form and fail at various depths in the bed during shearing. Newton's second law is used to calculate displacements along slip planes and the depth to which deformation extends in the bed. Consequent displacement profiles are convex upward, similar to those measured by Boulton and colleagues at Breidamerkurjökull, Iceland. The model results, when considered together with the long-term and widespread empirical support for Coulomb models in soils engineering, indicate that efforts to fit viscoplastic flow models to till displacement profiles may be misguided.