The dynamics of glacier motion is governed, to a large extent, by the properties of the basal interface. In this paper we address the interaction of a glacier with a layer of till at its bed in an attempt to test whether our physical understanding of till is sufficient to explain general features of the observed flow field and changes in geometry of Black Rapids Glacier, Alaska. We also investigate whether or not a till layer has a clear surface-observable signature in the dynamics of the glacier. Towards this end we use a finite element ice-flow model with a Coulomb failure criterion within the basal till layer. We find that simple 'till physics' can be used to describe decadal, seasonal, and short term (hours to days) velocity variations, and possibly uplift events. Mechanisms for each of these variations involve an increase in the extent of till at failure, a transfer of shear stress across the bed, and a consequent increase in ice deformation. 'Effective shape factors' are calculated to permit a simple incorporation of this boundary condition into glacier response models. Our analyses, however, have not resulted in the identification of a clear and unique signature of a till layer in the surface dynamics of the glacier.