In this paper, flow of viscous fluids across an array of solid and porous circular cylinders, which represents a porous media, is explored experimentally. The idealized array or bed of cylinders, which models tows and fibers in a fiber preform used in composites processing, was unidirectional consisting of either solid circular rods or porous circular bundles, By measuring the how rate and pressure drop across this bed of cylinders, we characterized the transverse permeability of the model porous media. In beds with porous bundles, the volume fraction inside the bundles ranged from 60 to 75% by packing 50-60 nylon fibers into 6.35 mm diameter holes. Both Newtonian and shear thinning fluids were used. These fluids were pumped through the medium such that the how was perpendicular to the fiber axes. Once the fiber bed was fully saturated, the permeability was determined with the aid of Darcy’s law. For the solid rods, the experimental results compare well with the asymptotic model recently developed by Bruschke and Advani For generalized Newtonian fluids. In addition, a heterogeneous fiber bed was constructed, consisting of fiber bundles in a regular array. During the filling stage, the progress of the flow front through the heterogeneous fiber beds was observed and the flow-induced void formation inside the fiber bundles was monitored. None of the existing permeability models could predict the permeability of the heterogeneous porous media. A series expansion was suggested to estimate permeabilities of such heterogeneous media.