This paper reports the results of a numerical investigation of the diffusion and reaction of methane in the washcoat of a catalytic monolith reactor. The kinetic rate expression used is an empirical equation determined experimentally for a palladium oxide catalyst. The effect of water inhibition on the reaction rate is included in the model. A multi-species diffusion and reaction model is used to simulate the process. The model is solved in a 2-D space using a finite element method. It is observed that the inhibiting effect of water tends to lower the observed reaction rate and that a higher surface water concentration results in an increase in the observed effectiveness factor. The effectiveness factor depends on three dimensionless parameters. Strong diffusion limitation can lead to high water concentrations at the interior of the catalytic washcoat.