The polar oceans contain sea ice of many thicknesses ranging from open water to thick pressure ridges. Since many of the physical properties of the ice depend upon its thickness, it is natural to expect its large-scale geophysical properties to depend on the relative abundance of the various ice types. The ice pack is treated as a mixture whose constituents are determined by their thickness and whose composition is determined by the area covered by each constituent. A dimensionless function g (h), the ice thickness distribution, is defined such that g (h) dh is the fraction of a given area covered by ice of thickness greater than h but less than h+dh. A theory is developed to explain how the ice thickness distribution changes in response to thermal and mechanical forcing. The theory models the changes in thickness due to melting and freezing and the rearrangement of existing ice to form leads and pressure ridges. In its present form the model assumes as inputs a growth rate function and the velocity field of the ice pack. The model is tested using strain data derived from the positions of three simultaneous manned drifting stations in the central Arctic during the period 1962--1964 and growth rates inferred from climatological heat flux averages. The results are compared with estimates of g based on submarine measurements of ice thickness.