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A mathematical model for oxidation catalytic reactor with secondary air injection that reduce carbon monoxide and hydrocarbon emission in automobile exhaust gas was developed and incorporated into the UMIST Spark-Ignition engine complete cycle Simulation program and the model was tested extensively against, experimental results. The rate of oxidation in the catalytic reactor was determined by the rate of mass transfer of the reactants to the catalyst surface and the rate of chemical reactions on the catalysts surface. The diffusivities of CO and HC in exhaust gases at different pressure, temperature and concentrations, required in the mass transfer rate calculations, we reevaluated by using statistical thermodynamics theory and rate of chemical reaction is calculated by using Arrhenius equation. In the pipe calculation, the method of characteristics was used. This method calculates pressure waves and considers the effect of gradual area changes, wall friction, heat transfer and entropy gradient. The heat of reaction generated by chemical reactions in the catalytic reactor was added to the existing path line and wave characteristics in the conventional form to evaluate pressure and temperature downstream of the catalytic reactor.