In this work, we formulate a model for the isothermal flow of a (basal) ice–till mixture that is overlain by a layer of pure ice. Such a model is relevant to the case of a glacier or ice sheet possessing a till at its base. To this end, ice is treated as usual as a constant true-density, very viscous fluid, while till, which is assumed to consist of sediment and bound (i.e. moving with the sediment) interstitial water, is also assumed in a first approximation to behave as such a fluid. Since the mixture is assumed isothermal, only the mass- and momentum-balance relations for till and ice need be considered. To complete the model, no-slip and stress-free boundary conditions are assumed at the base and free surface, respectively. By working with the former conditions, we neglect the process of entrainment of sediment into the basal layer, concentrating rather on its flow behaviour and thickness. The transition from the till–ice mixture layer to the overlaying pure ice layer is idealized in the model as a moving interface representing in the simplest case the till material boundary, at which jump-balance relations for till and ice apply. As in the basal layer, till and ice are assumed to interact mechanically at this interface. In the context of the thin-layer approximation, numerical solutions of the lowest-order form of the model show that it is predominantly the thickness of the basal (mixture) layer that is influenced by the ice–till momentum interaction.