In sea ice models with multiple thickness categories the ice thickness distribution evolves in time. The evolution of the thickness distribution as ice grows and melts is analogous to one-dimensional fluid transport and can be treated by similar numerical methods. One such method, remapping, is applied here. Thickness categories are represented as Lagrangian grid cells whose boundaries are projected forward in time. The thickness distribution is approximated as a linear or quadratic polynomial in each displaced category, and ice area and volume are transferred between categories so as to restore the original boundaries. In simple test problems and in a single-column model with forcing typical of the central Arctic, remapping performs significantly better than methods previously used in sea ice models. It is less diffusive than a scheme that fixes the ice thickness in each category and behaves better numerically than a scheme that represents the thickness distribution as a set of delta functions. Also, remapping converges faster (i.e., with fewer thickness categories) than the alternative schemes. With five to seven categories the errors due to finite resolution of the thickness distribution are much smaller than the errors due to other sources. Linear remapping performs as well as the more complex quadratic version and is recommended for climate modeling. Its computational cost is minimal compared to other sea ice model components. ¿ 2001 American Geophysical Union