The evolution and dynamics of the north-polar cap (residual-ice-cap/layered-deposits complex) of Mars is simulated with a thermomechanical ice-sheet model. We consider a scenario with ice-free initial conditions at 5 Ma before present due to the large obliquities which prevailed prior to this time. The north-polar cap is then built up to its present shape, driven by a parameterized climate forcing (surface temperature, surface mass balance) based on the obliquity and eccentricity history. The effects of different ice rheologies and different dust contents are investigated. It is found that the build-up scenarios require an accumulation rate of approximately 0.15-0.2 mm a −1 at present. The topography evolution is essentially independent of the ice dynamics due to the slow ice flow. Owing to the uncertainties associated with the ice rheology and the dust content, flow velocities can only be predicted within a range of two orders of magnitude.Likely present values are of the order of 0.1-1 mm a, and a strong variation over the climatic cycles is found. For all cases, computed basal temperatures are far below pressure melting.