An elementary reaction model of methane oxidation over gamma-Al2O3-supported palladium is developed by considering the phenomena of bulk reduction, hysteresis of catalyst activity, and negative activation during the re-oxidation. Validation of this model into a practical reactor with reverse flow operation is contained. Simulation results show residence time and full cycle time to be the predominating factors of temperature and reduction state distribution, respectively. Hysteresis of catalyst activity causes a vibrating pattern of outlet conversion, which is considered to go against industrial application.