This study analyses the influence of the random filament arrangement in fibre bundles on the resin flow behaviour. Transverse steady-state resin flow that occurs behind a liquid resin flow front was simulated numerically through statistically equivalent micro-structures at high-fibre volume fractions, Vf > 0.6, as observed in fibre bundles. The need of applying a minimum gap distance between neighbouring filaments was overcome by automated local mesh refinement. The derived permeability values showed significant scatter. Convergence of these values was determined at a ratio of flow length to filament radius greater than 20 for all three analysed fibre volume fractions. Mean permeabilities were between 6 and 10 times lower than those predicted for a hexagonal fibre array. A statistical model is proposed, which is able to predict the scatter of observed permeabilities based on simple micro-structural descriptors.