In recent years, to solve the problem of recycle and reuse of thermosetting composites, and to satisfy the needs for making of a wide variety of high performance composite products, studies on the development of the long fiber reinforced thermoplastic composites (LFRTPC) have been carried out very actively. A major problem in manufacturing LFRTPC by using pultrusion process is to uniformly and completely impregnate thermoplastic molten resin into the small gaps between the tightly packed reinforcing fibers because of their high viscosity. Hence, understanding of the fLow of molten resin through fibrous medium is very important to develop novel methods for impregnation. Moreover, it is impossible for us to design an optimum die without knowing the residence time to impregnate thermoplastic resin into fiber bundle. In response of this need, we have developed a semi-analytic model for predicting the transverse permeability for non-Newtonian fluid flow across arrays of aligned fiber bed. The flow behavior of non-Newtonian fluids with strongly shear thinning character was interpreted by using the finite element method from microscopic viewpoint, and then the transverse mobility, defined as the ratio of permeability and viscosity, of the cell was estimated by using Darcy's law.