Ice streams on the Siple Coast, West Antarctica, have a complex history of flow because their basal motion is governed by time-varying basal conditions. Although the mechanical interaction between ice and till is well established, very little is known about the potential effect of regionally scaled water transport in a basal water system, which has only recently become apparent. To investigate the combined effect of hydrological and mechanical processes, we developed the Hydrology, Ice and Till model, in which ice flow is coupled to a Coulomb-plastic till layer and a basal water system consisting of discrete conduits. When the model is applied to Kamb Ice Stream (KIS), results confirm that it is capable of oscillating between fast and stagnant modes of flow. We show that when subglacial conduits are disregarded or do not extend to the grounding line, the oscillatory behavior of the ice stream is governed by the basal thermal regime. When conduits extend to the grounding line, the modelled ice stream oscillation period is increased, peak speeds are reduced, and oscillations may ultimately cease if the volume of water supplied is sufficiently high. Three different hydrological states characterize the behavioral patterns of ice flow and these states are distinguished by conditions at the grounding line. Modelled ice stream velocities were found to oscillate with fast and slow periods typically lasting a few hundred years, although varying according to hydrological activity. Our results indicate that KIS could reactivate this century, given its hydrological setting and ~170 years of stagnation.