Some catalysts such as copper zeolites have shown promise for direct NO decomposition and selective NO reduction via hydrocarbons in lean exhausts. This paper describes modeling calculations for the performance of a Cu-ZSM-5 NOx reduction catalyst. The numerical model simulates the multi-component transport and reaction processes that occur within a catalyzed monolith support. The surface boundary conditions for the reacting species are satisfied through use of multi-dimensional Newton-Raphsson iteration. The model is used to formulate global rate expressions for the oxidation of C3H6 and the reduction of NO by adjusting kinetic parameters until predicted conversion efficiencies match experimental data. Then the numerical model is compared to data from higher space velocities to test the validity of the kinetic model. The comparison at higher space velocity shows reasonable agreement, although additional optimization of the kinetic parameters is possible. The simulated interactions within the catalytic passage demonstrate important features of the selective NO reduction and show that optimal lean NOx catalyst performance may require high transport rates of the reductant species to the catalyst surface.