We apply a coupled model of ice sheet dynamics and subglacial hydrology to investigate the dynamics and future evolution of the Vatnaj¿kull 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 Vatnaj¿kull, with and without longitudinal stress effects. Equilibrium ice cap configurations exist for Vatnaj¿kull but under a narrow range of climatic boundary conditions. Equilibrium reconstructions have an average ice thickness greater than what is observed at Vatnaj¿kull, consistent with our inability to capture surge dynamics in Vatnaj¿kull's outlet glaciers. Hydrological regulation of basal flow, longitudinal stress coupling, and a simple parameterization of the subglacial heat flux from Vatnaj¿kull's geothermal cauldrons all help to reduce average ice thickness in the equilibrium reconstructions, but cases that reproduce the present-day ice volume have an ice cap area that is 5--10% less than the actual ice cap. Present-day reconstructions that adopt a realistic climate spin-up for the period 1600--1990 provide improved fits to the modern-day ice cap geometry. This indicates that climatic disequilibrium also plays a significant role in dictating Vatnaj¿kull's morphology. Simulations for the period 1600--2300 illustrate that air temperature is the dominant control on Vatnaj¿kull's volume and area. Longitudinal stress coupling and hydrological coupling both increase Vatnaj¿kull's sensitivity to future warming.)