A new ray-tracing method for the calculation of collision probabilities within arbitrary three-dimensional geometries has been developed. This method is used to discretize the neutron transport equation for heterogeneous rectangular cells containing zones of mixed cylindrical and rectangular geometry. For multicell applications, the interface current (IC) method provides the coupling between cells. The solution to the IC equations over multicell domains consisting of rectangular three-dimensional cells is improved by using an alternate direction implicit iteration scheme with variational acceleration. Results include comparisons of this technique with SHETAN for simple geometries and the analysis of a three-dimensional extension of a two-dimensional 15 × 15 pressurized water reactor benchmark problem.