A good understanding of woven fiber preform permeabilities is critical in the design and optimization of the composite molding processes encountered in resin transfer molding (RTM); yet these issues remain unresolved in the literature. Many have attempted to address permeability predictions for flat undeformed fiber preform, but few have investigated permeability variations for complex geometries of porous fibrous media. In this study, the objectives are to: (i) provide a brief review of existing methods for the prediction of the fiber mat permeability; (ii) postulate a more realistic representation of a unit cell to account for such fabric structures as crimp, tow spacing and the like; and (iii) apply computational approximations to predict effective permeabilities for use in modeling of structural composites manufacturing processes. The Stokes equation is used to model the flow in the inter-tow region of the unit cell, and in the intra-tow region, the Brinkman's equation is used. Initial permeability calculations are performed for a three-dimensional unit cell model representative of the PET-61 woven fabric composite. The results show good agreement with experimental data published in the literature.