The aim of the present work is to investigate the low rate/pressure gradient relationship for the low of yield stress luids through rectilinear capillaries of non-circular cross-sections. These capillaries very often serve as basic elements in the modeling of porous media as bundles of capillaries or pore-network models. Based on the notions of shape coeicient and critical Bingham number, empirical low rate/pressure gradient relationships have been proposed for both Bingham and Herschel-Bulkley luids. The reliability of these relationships has been assessed by performing numerical simulations with the open-source Computational Fluid Dynamics (CFD) package OpenFOAM. For the considered cross-sectional shapes (equilateral triangle and square), and for a wide range of Bingham numbers, the predictions of the proposed empirical relationships have shown to be in very good agreement with the results of the current numerical simulations, as well as with previous results from the literature. An interesting feature of the proposed empirical relationships is the possibility to easily predict the total low rate under a given imposed pressure gradient in a bundle of non-circular capillaries having any random distribution of inscribed circle radii. Furthermore, in the context of the yield stress luid porosimetry method (YSM), experimental data may now be processed based upon bundles of capillaries with non-circular cross-sections.