The thickness distribution of sea ice is maintained by a balance of thermal and mechanical processes. Observations now exist that make it possible to quantify this balance and to test models of the individual physical processes. In particular, the observed distributions, used with fairly well established thermodynamic growth rates, give an estimate of the redistribution process that models the formation of pressure ridges. To highlight the main ideas, the evolution of the thickness distribution is recast as a Markov process forced by the mean velocity divergence and a measure of the random short term deformation. This model reproduces features of the observed thickness distribution such as the peak near 3 m, the mean thickness somewhat greater than 3 m, the long tail, and the variable shape of the thin side of the distribution. Analytical expressions for the mean and variance of the ice thickness are given, showing how they depend on the growth rates for the thick and thin ice, the equilibrium thickness, the ice deformation, and the rule of building pressure ridges. These are sensitive to the mean divergence and the melt rate for thick ice. With large amounts of data now available for both the ice thickness and the ice motion, further progress is anticipated toward understanding the process which shape the thickness distribution.