The lattice Boltzmann (LB) method has been used to simulate, at the pore scale, the flow of non-Nexnonian fluids through complex random porous media in both two and three dimensions. We focus our work oil power-law fluids with index n < 1 (shear-thinning), though the method is sufficiently general to include other stress-shear rate relationships. Simulated results of flux versus driving force show excellent agreement with established theory, provided sufficient lattice resolution is used. In this respect we explore and quantify the relationship between lattice resolution and simulation accuracy as a function of it. (c) 2005 Elsevier B.V. All rights reserved.