Two- and three-dimensional diffusive flow behavior in a coated dense layer of a composite membrane or in a dense polymer membrane placed adherently on a mechanical porous support in a permeation test cell was analyzed and compared to clarify the extent of decrement in flux compared with the case without support. By solving two- and three-dimensional models proposed to describe the flow in the coated dense layer, steady-state concentration profiles of fluid and total diffusive flux were calculated. As a result, the flux decreased with decreasing ratio of membrane thickness to width of unit porous support, t(m)/w(u), and with decreasing porosity of support, epsilon. The three-dimensional analysis was found to better realize the flow in the dense layer supported on porous material. Such a decrease in flux could be represented by flux ratio, f, which was found to be approximated by the following semi-empirical formula as a function of t(m)/w(u) ratio and epsilon.