This paper presents a computational investigation on the influence of the meso- (inter-tow; phi(i)) and micro-scale (intra-tow; phi(t)) porosities on the effective transverse permeability (K-p) of square arrays of permeable fiber tows. The equations governing Stokes flow are solved, using the Boundary Element Method, in unit cells which consist of a number of fiber-like filaments, arranged in square packing within the circular perimeter of the tow. The key finding of this study is that the permeability ratio (K-p/K-s), where (K-s) is the permeability of the corresponding square array of impermeable tows, can be described as a power-law function of the effective intra-tow porosity (chi). Based on this, a scaling is proposed according to which the computational results for K-p at relatively low Values of the inter-tow porosity (0.25 < phi(i) < 0.5) collapse on a power-law curve with exponent 2.1 when plotted against (chi).