The flow of non-Newtonian fluids in packed beds and other porous media is important in several applications such as polymer processing, filtration, and enhanced oil recovery. Expressions for flowrate versus pressure gradient are desirable for a-priori prediction and for substitution into continuum models. In this work, physically representative network models are used to model the flow of shear-thinning fluids, including power-law and Ellis fluids. The networks are used to investigate the effects of fluid rheology and bed morphology on flow. A simple macroscopic model is developed for the flow of power-law and Ellis fluids in packed beds using results from the network model. The model has the same general functionality as those developed using the popular bundle-of-tubes approach. The constant which appears in these models, is often directly derived from the tortuosity and a simple representation of the porous media. It is shown here that this can lead to incorrect and ambiguous values of the constant. Furthermore, the constant is a weak function of the shear-thinning index, indicating that no single bundle-of-tubes could ever properly model flow for a wide variety of shear-thinning fluids. The macroscopic model is compared to experimental data for shear-thinning fluids available in the literature. The model fits the data well when beta is treated as an experimental parameter. The best-fit values of beta vary, which is expected because even the constant C in the Blake-Kozeny equation varies depending on the source consulted. Additionally, physical effects, such as adsorption and filtration, as well as theological effects such as viscoelasticity may affect the value of beta. We believe that in the absence of these effects, beta equals approximately 1.46 for packed beds of uniform spheres at relatively moderate values of the shear-thinning index (> 0.3). (c) 2005 Elsevier Ltd. All rights reserved.