This paper presents a model using the self-consistent method for estimating the resin flow permeability of fiber tow preforms. The permeable resin is assumed to be a Newtonian fluid, such as an uncured and low viscosity epoxy resin. Permeability in both longitudinal and transverse directions is considered. In the discussion, a basic cell insertion is constructed to include a representative fiber tow surrounded with fluid. The insertion is placed into a homogeneous medium with an unknown permeability. Stokes flow is applied to the fluid region, and Darcy flow is considered at the tow region and in the outside homogeneous medium. Boundary and interface conditions as well as consistent conditions, including the total amount of the flow and the dissipation energy, are applied accordingly. Permeability is solved from these considerations. The prediction expressions using parameters of average fiber volume fraction, tow volume fraction, and tow size are derived. The results show that the main flow paths are the openings or gaps between neighboring tows in both longitudinal and transverse directions. The observation provides a scientific base for the simplification of the problem treatment.