Abstract Lean burn after-treatment systems are the current focus for reducing emissions from diesel exhaust. The trend is for commercial CFD packages to use a single channel modelling approach. Due to computational demands, this necessitates specification of representative channels for modelling, implying prior knowledge of the flow field. This paper investigates a methodology for applying the porous medium approach to lean burn after-treatment systems. This approach has proved successful for three-way catalysis modelling and has the advantage that the flow field is predicted. Chemical kinetic rates for NO x trapping and regeneration in the model are based on information available in the open literature. Similarly, filtration information based on mass accumulation and soot combustion kinetics are also readily available. Modification of the source terms in a commercial CFD package enables prediction of trapping and release of NO x . This is an effective way to model a NO x trap after-treatment system and provides simultaneous 3D modelling of the flow field. With diesel, particulate filtration is required. In the case of particulate traps, however, because of channel geometry, some assumptions are necessary for use of the porous medium approach and these are discussed in this paper. Both models produce qualitatively correct output and have parameters that can be tuned to conform to experimental data. Data to validate the NO x trap model is to be measured. The particulate trap model, on the other hand, is a feasibility study for modelling the complete diesel after-treatment system using the porous medium approach.