Viscous flow in certain symmetrical ducts can be solved by a modified Levy＇s method with internal matching. The method is simple, efficient and accurate. Approximate analytic formulas are also derived for the extreme cases. It is found that cutting convex corners has little effect on the flow rate, but a centered core, however slender, decreases flow dramatically. The graphs for flow rates are useful for the design of ell, cross and nested square ducts and also for the prediction of the permeability of parallel-structured porous media.