The present work considers the capillary flow of Newtonian fluids along a single fibre yarn and through a plain-woven fabric. In the first case, one-dimensional Darcy's flow is considered through the micro-pores of the fibre yarns. In the second case, two-dimensional in-plane network infiltration is considered through the micro-pores of the network of fibre yarns in the fabric. In both cases predictions include the infiltration length as a function of time, the apparent permeability and the capillary pressure. The latter case also includes the number of unsaturated transverse yarns and the degree of saturation. All predictions are compared to experimental measurements and the agreement is very good.