Abstract The majority of complex fluids used in oil-field applications are polymeric solutions exhibiting shear-thinning (pseudoplastic) behavior in solution. We study the flow of power-law fluids in porous media using network modeling. We use realistic representations of porous media that capture the geometry and topology of sands and sandstones as input to our flow model. The bulk rheology (variation of viscosity with shear rate) is used to define a relationship between pressure drop and average flow velocity in each pore. We then compute the variation of average velocity with apparent viscosity for the whole network. We successfully predict the results of four experiments from different sources in the literature. The predictions are superior to those using simplified capillary bundle models and involve no adjustable parameters, but are limited to polymer exhibiting simple shear-thinning behavior and require a detailed description of the pore space of interest.