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Experiments beneath Breidamerkurjökull in Iceland have led to development of flow laws for the subglacial till, relating strain rate to shear stress and effective pressure and assuming either Bingham fluid or nonlinearly viscous fluid behavior. Water pressures in the till are less than ice pressures and it is suggested that this may lead to infiltration of ice into the sediment, which inhibits sliding at the ice/sediment interface. Where water pressures are equal or near to ice pressures, infiltration does not occur and sliding may result. A one‐dimensional theory of subglacial deformation is developed in which the empirical flow law is coupled with a model of subglacial hydrology and consolidation. This predicts stable states in which subglacial sediment either does not deform or a dilatant deforming horizon forms with positive effective pressures at the ice/bed interface or unstable states where zero or negative effective …