The out-of-plane permeability of 25 mm-long chopped glass fibre bundle beds was measured. These bundles, used in sheet moulding compound (SMC) composites, have an elliptical cross-section with the major axis perpendicular to the flow direction. An adapted experimental set-up was developed, which prevented flow along the sides of the packed bundle bed. The set-up was tested with needled glass fibre mats, and satisfactory agreement was found with previous results. The transverse permeability of the loose SMC bundle beds was then measured and linked to the bundle sizing type, geometry and volume fraction. Finally, the results could be well described by models taking into account the elliptical nature of the bundles.