A new pseudo-continuous model, describing the fluid flow through packed bed reactors, is developed by formulating the Navier-Stokes equations for a statistically described domain geometry. A coupling term, occurring in the momentum equation, represents the fluid-solid interaction and is modelled by comparison with the exact Navier-Stokes equations. Static and dynamic, inviscid and viscous contributions are separated, and stringent requirements for the dependence on the local voidage are found which are met by a simple model. Good agreement with correlations and experiments is found for the predictions of the pressure drop and the radial distribution of the axial velocity. (c) 2005 Elsevier Ltd. All rights reserved.