Several numerical simulations of the Arctic ice cover over a seasonal cycle are carried out. Two different types of constitutive laws are examined: rigid plastic and linear viscous. In both cases, the strength of the ice interaction is taken as a function of ice thickness and compactness. The thickness and compactness, in turn, evolve according to continuity equations which include thermodynamic source and sink terms. The simulations with the rigid-plastic law reproduce reasonable geographical ice-thickness variations, ice outflow, and ice-velocity characteristics. The viscous simulations (especially the Newtonian viscous case) produce less satisfactory geographical ice thickness variations, and near-shore velocity characteristics. In addition the Newtonian-viscous simulation produces highly unrealistic ice-edge effects in summer. The results are discussed in terms of the relative magnitudes of the shear and compressive strengths, and in terms of the non-linear versus linear dependence on deformation in the ice rheology. The portion of this study employing a plastic constitutive law is published in full in Journal of Physical Oceanography, Vol. 9, No. 4, 1979, p. 815–46.