The MPACT code is being jointly developed by the University of Michigan and Oak Ridge National Laboratory. It uses the 2-D/1-D method to solve neutron transport problems for reactors. The 2-D/1-D method decomposes the problem into a stack of 2-D planes and uses a high-fidelity transport method to resolve all heterogeneity in each plane. These planes are then coupled axially, using a lower-order solver. With this scheme, three-dimensional (3-D) solutions to the transport equation can be obtained at a much lower cost. The 2-D/1-D method assumes that the materials are axially homogeneous for each 2-D plane. Violation of this assumption requires homogenization, which can significantly reduce the accuracy of the calculation. This paper presents the subray method of characteristics (subray MOC) as a solution to this problem. Subray MOC is a subgrid method that allows local heterogeneities to be directly resolved by method of characteristics while treating the rest of the 2-D plane as axially uniform. This improves the accuracy in the neighborhood of the heterogeneity while minimizing the increase in run time. The method was applied to variations of the C5G7 benchmark problems and compared with a previously developed subgrid method called the subplane collision probabilities (SCP) method. Comparisons were made among results obtained using subray MOC, the SCP method, and no subgrid method. Subray MOC consistently performed best, reducing maximum 3-D power distribution errors from as high as 30% to 2% or less. Furthermore, it consistently outperformed the SCP method with run times that were shorter than the reference calculations.