Numerical simulations bf catalytic oxidation in monolith reactors are performed in order to develop criteria for mass transfer limitation. A two-dimensional finite-element simulator previously developed is used to examine previously reported studies of propane and carbon monoxide combustion in excess oxygen. The Sherwood and Nusselt numbers computed from the two-dimensional simulation results are compared to numbers derived experimentally. The results from the simulations are much higher than results which have been reported in the literature for experimental work. Simulation results agree well with numbers obtained analytically and experimentally for non-reacting flow in circular tubes, and also with other correlations for reacting flows based on numerical work. The reason for the discrepancy between experimental and simulated results is explained. For first-order reactions, a dimensionless catalytic reaction number is proposed, which may be used to evaluate whether or not the rate is mass transfer controlled. For the oxidation of CO, multiple steady states are possible and the variation in Nusselt and Sherwood numbers under transient conditions is discussed. The influence of diffusion in a real monolith washcoat is also examined. In square monolith channels of dimension 1 mm, low effectiveness factors are obtained for temperatures above 700 K, and much of the catalyst is not utilised. It is shown that care needs to be taken in the extension of relatively low-temperature kinetic data to the elevated temperatures encountered in real operating conditions.