A theory describing evolution of the ice thickness distribution (the probability density of ice thickness) was proposed by Thorndike et al. (1975) and has been used in several sea ice models. The advantage of this theory over the widely used two-level formulation is that it treats ridging explicitly as a redistribution of ice thickness, and ice strength as a function of energy losses incurred by ridge formation. However, the parameterization of these processes remains rather speculative and largely untested, and so our purpose here is to explore these parameterizations using a numerical model based on this theory. The model uses a 160-km resolution grid of the Arctic and 7 years of observed atmospheric forcing data (1979--1985). Monthly oceanic heat flux and current fields are obtained from a 40-km resolution coupled ice-ocean model run separately with the same forcing. By requiring the computed monthly mean ice drift to have the same magnitude as observed buoy drift, we estimate the primary strength parameter: the ratio of total to potential energy change during ridging. This ratio depends on the value of other parameters; however, the standard case has a ratio of 17 which is within the range estimated by Hopkins (1994) in simulations of individual ridging events. The effects of ridge redistribution and shear ridging parameters are illustrated by a series of sensitivity studies and comparisons between observed and modeled ice thickness distributions and ridge statistics. In addition, these comparisons highlight the following shortcomings of the thickness distribution theory as it is presently implemented: first, the process of first-year to multiyear ridge consolidation is ignored; and second, the observed preferential melt of thick ridged ice is not reproduced. ¿ American Geophysical Union 1995