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We apply a coupled model of ice sheet dynamics and subglacial hydrology to investigate the dynamics and future evolution of the Vatnajökull ice cap, Iceland. In this paper we describe a new theoretical approach to introducing longitudinal stress coupling in the ice dynamics solution, and we analyze our ability to simulate the main features of Vatnajökull, with and without longitudinal stress effects. Equilibrium ice cap configurations exist for Vatnajökull but under a narrow range of climatic boundary conditions. Equilibrium reconstructions have an average ice thickness greater than what is observed at Vatnajökull, consistent with our inability to capture surge dynamics in Vatnajökull's outlet glaciers. Hydrological regulation of basal flow, longitudinal stress coupling, and a simple parameterization of the subglacial heat flux from Vatnajökull's geothermal cauldrons all help to reduce average ice thickness in the …