Abstract A mathematical model is developed for the simulation of the chemical and transport phenomena in three-way catalysts for natural-gas vehicles, with honeycomb and foam substrates. The chemical phenomena are modelled on the basis of a simplified approach, which assumes that pollutant conversion is governed by oxygen storage and release dynamics. The transport phenomena, i.e. heat transfer, gas-phase mass transfer, washcoat diffusion, and pressure drop, are modelled on the basis of correlations adapted from the literature. The model is validated using lambda scan tests and a cold-start driving cycle, carried out with a honeycomb catalyst and a ceramic foam catalyst. The experimental data show a decline in methane conversion for lean mixtures, which is modelled by an inhibition term of methane oxidation from nitric oxide. The proposed model may capture the performance of both substrates with sufficient accuracy, both under cold-start and under hot-mode conditions. The model-based comparison of the two substrates shows that the ceramic foam presents inferior carbon monoxide conversion in the extra-urban part of the cycle. Although the gas-phase mass transfer in the ceramic foam is faster than with the honeycomb monolith, diffusion in the washcoat pores is much slower. As a result, the mass-transfer-limited conversion efficiency of the foam is lower. This is primarily attributed to the higher washcoat thickness of the foam sample tested.