The permeability of an idealized unidirectional reinforcement consisting of regularly ordered, parallel fibres is derived starting from first principles (Navier-Stokes equations) both for flow along and for flow perpendicular to the fibres. First, an approximate analytical solution for transverse flow is derived which differs from the Kozeny-Carman equation for the permeability of a porous medium in that the transverse flow stops when the maximum fibre volume fraction is reached. The solution for flow along the fibres has the same form as the Kozeny-Carman equation. A comparison shows excellent agreement between a numerical solution of the full flow equations and the approximate one at medium to high fibre volume fractions (Vf > 0.35). The theoretical predictions of permeability were tested in a specially designed mould. The results from the experiments with an unsaturated polyester resin (Jotun PO-2454) and the unidirectional reinforcement did in all cases show excellent agreement with results predicted by Darcy's law (the square of the flow front position increases linearly with time if the injection pressure is kept constant). The theoretical model could be fitted to the experimental data both for flow along the fibres and for cross flow based on data for flow along the fibres only. The fitting is obtained by adjusting one parameter in the model, the effective fibre radius, to a value about four times larger than the real fibre radius (15 μm). Scanning electron microscopy shows that the fibres are arranged in bundles looking like cylinders with ellipsoidal cross section which may be the explanation for the effective fibre radius in the fitted model equation being larger than the real fibre radius.