An analytical expression for the threshold pressure of capillaries with irregular polygonal cross section is obtained using the MS-P method. The cases of a regular polygonal, an arbitrary triangular, and a rectangular cross section are obtained as particular cases of the general expression. Some regularities of the threshold pressure with the shape factor and the wetting phase saturation for different capillary geometries are reported. The derived expressions are valid for any value of the contact angle and can be used directly in a pore network simulator.