An apparent permeability of an idealized unidirectional reinforcement is derived for power-law fluid flow perpendicular to the fibers. The reinforcement consists of regularly ordered, parallel fibers arranged in a quadratic or hexagonal pattern. The expression is obtained starting from first principles for low Reynolds number, incompressible and isothermal flow and is expressed in terms of the radius of the fibers, the fiber volume fraction, and the power-law index. The model is successfully verified with computational fluid dynamic simulations. © 2006 SAGE Publications.