The combustion of methane on a palladium catalyst was examined in a monolith reactor. The rate equation was determined and showed an approximately first order dependence in methane concentration and zero order dependence on oxygen concentration. Significant inhibition by water was observed, and inhibition by carbon dioxide was negligible. At high water concentrations the order with respect to water is approximately minus one. A significant reduction in both activity and activation energy was observed above temperatures of approximately 820 K with a dry feed. Significant diffusion limitation in the washcoat was observed. The intrinsic volumetric rate constant was found to be directly proportional to the palladium loading of the washcoat. The effect on the reaction rate of layers of inert washcoat placed on top of the active catalyst was investigated. These diffusion barriers reduced the reaction rate. The reactor performance was modelled using a two-dimensional finite element single channel model that included washcoat diffusion. The effect of diffusion barriers was compared to the effect of using a less active catalyst for steady state and transient modes of operation at values of the Lewis number. At low Lewis number the diffusion barrier was effective at reducing the temperature rise at the entrance to the reactor for large inlet reactant concentration.