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The numerical predictions of the velocity field and the component of longitudinal permeability in the filtration equation for the steady incompressible the Sisko and the Carreau fluid flow through the assemblages of cylindrical fibers are presented.The fibers are arranged regularly in triangular,square,and hexagonal arrays.Flow is longitudinal with respect to the fibers.The non-linear governing equation in the repeated element of the array is solved using the Picard iteration method.At each iteration step the method of fundamental solutions and the method of particular solutions are used.