The effect of paper structure on flow characteristics of various fluids is one of the most important, fundamental problems in papermaking, coating, and printing. A computer code based on a cellular automaton model, in particular the lattice-gas Boltzmann model, has been developed to simulate flow numerically in a random fibre network. As a preliminary investigation, a numerical experiment has been conducted on the three-dimensional permeability of an interpenetrable fibre network. It was found that the in-plane permeability and the z-directional (thickness direction) permeability are very sensitive to the distribution of fibre segments in the z-direction. At a constant porosity, the z-directional permeability increases and the in-plane permeability decreases with increasing z-directional fibre orientation.