The ice-till mixtures at the base of glaciers and ice sheets play a very important role in the movement of the glaciers and ice sheets. This mixture is modelled as an isothermal flow which is overlain by a layer of pure ice. In this model, ice is treated as usual as a very viscous fluid with a constant true density, while till, which is assumed to consist of sediment and bound (that is, moving with the sediment) interstitial water and/or ice, is also assumed in a first approximation to behave such as a fluid. For an isothermal flow below the melting point the water component can be neglected. Therefore, only the mass and momentum balances for till and ice are needed. To complete the model, no-slip and stress-free boundary conditions are assumed at the base and free-surface, respectively. The transition from the till-ice mixture layer to the overlying 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. The mechanical interactions are considered in the mixture basel layer, as well as at the interface via the surface production. The interface mechanical interaction is supposed to be only a function of the volume fraction jump across the interface. In the context of the thin-layer approximation, numerical solutions of the lowest-order form of the model shaw a till distribution which is reminiscent to the ice-till layer in geophysical environment.