In an attempt to reduce particulate and NOx emissions from Diesel exhaust, the combined DPF and SCR filter is now frequently chosen as the preferred catalyst. When this device functions effectively it saves valuable packaging space in a passenger vehicle. As part of its development, modelling of its emissions performance is essential. Single channel modelling would seem to be the obvious choice for an SCRF because of its complex internal geometry. This, however, can be computationally demanding if modelling the full monolith. For a normal flow-through catalyst monolith the porous medium approach is an attractive alternative as it accounts for non-uniform inlet conditions without the need to model every channel. This paper attempts to model an SCRF by applying the porous medium approach. The model is essentially 1D but as with all porous medium models, can very easily be applied to 3D cases once developed and validated. The model is described in full in this paper and values for all the key parameters are presented. The filter is assumed to collect soot in the inlet channels, but only the outlet channels are coated with SCR washcoat, as in the most recent devices. This aims to avoid back diffusion of NO2 that promotes soot and NOx reactions. But it is necessary to modify the pressure loss expression term to account for the smaller size of the washcoated outlet channel. The SCR model integrated into the CFD coding is simple and based on a scheme available in the literature. This includes the standard and fast SCR reactions and ammonia adsorption and desorption. NO and ammonia oxidation are also included and are important during the high temperature regeneration phase. The detail of the flow at the channel scale is not modelled but the species can be modelled at the channel scale for the monolith by application of source terms in the species transport equation. The source terms are evaluated in user subroutines in commercial CFD software. The species levels of NO, NO2 and NH3 in the flow coming through the filter wall, in the pores in the wall and in the flow in the downstream channel are all modelled as a function of distance along the brick. The simplifying assumptions on which this model is based are stated in this paper. The model produces plausible output when run as a demonstration case for a 1050 s soot storage period at 550 K, followed by a 150 s regeneration period at 900 K, and then for a further soot storage period at 550 K. The simulations are in qualitative agreement with the expected performance of a combined DPF and SCR in a real Diesel exhaust. An attempt has been made to apply the model to a real case based on data available in the literature so that its output can be validated.