Network modeling has been performed to obtain quantitative and predictive results of the flow of yield-stress fluids in packed beds. Physically representative networks were used as the basis for the modeling, which have a one-to-one correspondence to computer-generated packed beds of spheres. The networks are able to account for the interconnectivity, heterogeneity, and converging/diverging geometry that are inherent in porous media. The approach can be used to model a wide range of non-Newtonian fluids, but the emphasis is for yield-stress fluids that can be represented using a Binghani model. For these fluids, a threshold pressure gradient is required to initiate flow, and flow at low pressure gradients is characterized by critical percolation behavior. Quantitative results of superficial velocity vs. pressure gradient are presented, and are compared to traditional bundle-of-tubes models, as well as limited experimental data available in the literature. Important differences are observed between the network model and the constitutive models. These are attributed mainly to heterogeneity and converging/diverging geometry, which are not accounted for in the semiempirical models. Comparison to experimental data is good for certain fluids. In other cases, the modeling suggests that effects other than fluid rheology may also have affected flow, such as adsorption or filtration. (C) 2004 American Institute of Chemical Engineers.