A new way of calculating the airflow resistivity of randomly placed parallel cylinders is presented. The calculation is based on Voronoi polygons, and the resistivity is given by the mean spacing between the fibers, their diameters, and the physical properties of air. New explicit formulas for the resistivity are given, which are valid for the cylinder (fiber) concentrations found in acoustic materials. A one-dimensional model consisting of parallel plates with random spacing between the plates is first discussed. Then a two-dimensional model consisting of parallel cylinders randomly spaced is treated for flow parallel and perpendicular to the cylinders. The resistivity formulas are exact for plates and approximate for cylinders.