Subglacial hydrology is known to influence the flow of ice. However, difficulty in accessing the base of large ice sheets has made determining the interaction between ice streams, basal sediment and water difficult to discern. The aim of this thesis is to determine the influence of subglacial hydrology on the flow of the West Antarctic ice streams. This is achieved through development of a numerical flowline model, the Hydrology, Ice and Till (HIT) model. Ice thermodynamics are coupled to a till layer of Coulomb plastic rheology. The porosity of the till changes with basal melt and freeze and can be augmented by water transported through a subglacial conduit system. Water availability strongly affects ice flow, as till porosity influences the till failure strength and thereby the basal resistance of the ice. The model was developed in four stages and a number of sensitivity tests were performed. It was then applied to Kamb Ice Stream (Ice Stream C) and Whillians Ice Stream (Ice Stream B), West Antarctica. Results confirm that ice streams are capable of oscillating between fast and slow velocity states. Cycles are generated at the grounding line of an ice stream and the speed of the transition from slow to fast flow is governed by water availability. The period of oscillation of the cycles for the West Antarctic ice streams was found to be several hundred years, which is in line with observations of stagnation and reactivation of these ice streams. This shows that subglacial hydrology has a role in modulating the flow variability of ice streams and that rather large changes in the flow of the West Antarctic ice streams are likely to occur this century.