A one-dimensional ocean model, coupled with an ice model where the ice cover is partitioned into a number of thickness categories, is used to investigate how the ice thickness distribution in the Arctic Ocean depends on the two deformation processes, export (net divergence) and ridging. The model standard case generates vertical profiles of temperature, salinity and an ice thickness distribution similar to the observations. The standard case oceanic heat flux agrees well with recently deduced heat fluxes from Arctic Ice Dynamics Joint Experiment (AIDJEX) data. The oceanic heat flux is about 18 W m−2 during summer and about 1 W m−2, during winter. It is found that the mean ice thickness decreases with increasing ice export in close agreement with other investigations. However, the dependence of the mean ice thickness on ridging activity is found to be very weak. The change of the mean ice thickness is only 12 cm when increasing the ridging activity in the model from 0 to 0.4 yr−1; where the larger value represents an estimate of the actual ridging activity in the Arctic Ocean. In a sensitivity study, different types of ridging and albedo parameterizations are tested, and this weak dependence is found to be very robust. Other properties of the model ice cover are sensitive to ridging though: The equilibrium thickness of undeformed ice decreases with both export and ridging activity. The annual maximum open water fraction and the amplitude of the seasonal thickness variation increases with export and ridging.