Because of the increasing use of polymer composites in a wide variety of industrial applications, the manufacturing of complex composite parts has become an important research topic. When a part is manufactured by liquid composite molding (LCM), the reinforcement undergoes a certain amount of deformation after closure and sealing of the mold. In the case of bidirectional woven fabrics, this deformation may significantly affect the resin flow and mold filling because of changes in the values of permeability. Among other considerations that govern the accuracy of numerical simulations of mold filling, it is important to predict the changes of permeability as a function of the local shearing angle of the preform. The resin flow through a fibrous reinforcement is governed by Darcy's law, which states that the fluid flow rate is proportional to the pressure gradient. The shape of the flow front in a point-wise injection through an anisotropic preform is an ellipse. Part I of this article describes a new methodology based on the ellipse equation to derive the in-plane permeability tensor from unidirectional injection experiments in deformed woven fabrics. Part II presents a mathematical model that predicts the principal permeabilities and their orientation for sheared fabrics from the permeability characterization of unsheared fabrics. Unidirectional flow experiments were conducted for a nonstitched, balanced, woven fabric for different shearing angles and fiber volume fractions. This article presents experimental results for deformed and undeformed fabrics obtained by unidirectional flow measurements. A comparison of the proposed characterization methodology with radial flow experiments is also included. POLYM. COMPOS., 28:797-811, 2007.