The application of the cell discretization (CD) method to a class of nuclear reactor problems is described. The CD method is based on partitioning the domain in which the diffusion equations are to be solved into a set of subdomains, or “cells.” This approach, which resembles that used in the finite element method, nevertheless differs from it in certain important respects, some of which are mentioned in the course of describing CD. A FORTRAN program has been written that implements many of the features of the CD method, but is restricted to rectangular geometry. Several representative problems from the literature are solved numerically with CD, and the results are compared with the published ones. The central processor unit times are given for solution of these problems on the IBM 370/158 under VM, a time-sharing system. All results, including keff, peak-to-average-power ratios, integrated fluxes, etc. are listed in tables in such a way as to make comparison convenient. Flux plots are also shown for those cases where they were given in the literature.