Over the past twenty years, several computer models for structured catalytic reactors such as the monolith converter have been developed with various levels of complexity and accuracy. Despite the availability of faster and faster computers, no reports have been made yet on the successful simulation of transport phenomena in every channel of a monolith catalytic converter by means of a full three-dimensional discrete model. The purpose of this work is to show the potential of such a model, based on the lattice Boltzmann method (LBM), for simulating fluid flow in an elliptical shaped honeycomb monolith reactor comprising a total of 7539 parallel channels. This example of industrial relevance will serve to evidence the progress made in computer modeling in recent years, but also to bring up aspects that need to be further improved, such as the use of LBM to simulate efficiently turbulent flow and heat and mass transfer in this type of structured catalytic reactors. (C) 2011 Elsevier B.V. All rights reserved.