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This paper presents a numerical solution of longitudinal fluid flow in a porous media consisting of regularly distribute parallel fibers.On the base of this longitudinal permeability and the effective viscosity for the Brinkman filtration equation as a function of fiber packing geometry,the fiber volume fraction and properties of a fluid are determined.Fibers are arranged in a square and a triangular arrays.The effective viscosity is determined for system of the fibers placed between two parallel walls.The Newtonian fluid and the generalized Newtonian,namely the power-law model,the Sisko model and the Carreau model are considered.Both the method of fundamental solutions(MFS)and the special purpose Trefftz functions(SPTF)are used for solution of the micro-structural flow problem for the Newtonian fluid are applied.For the generalized Newtonian fluids the MFS,the method of particular solutions(MPS)and the Picard iteration method are applied.