In this paper, the normal flow permeability of an ordered fibrous structure, with square cross section is determined analytically. Porous structure is represented by a “unit cell” which is assumed to be repeated throughout the media. The selected unit cell is the space between four cylinders with square cross section. The analytical solution leads to a closed form equation for normal permeability of porous media including the geometrical parameters. Due to lack of experimental and analytical data for fluid flow through square cross section structures, a numerical study is also done and the obtained results are compared with the analytical solution. Moreover, a suitable scale analysis approach is employed to estimate the permeability of the fibrous structure. The presented method can predict the permeability of fibrous media, especially at high porosity. The present solution is successfully compared with the existing model in the literature over a wide range of porosity.