A method for the numerical simulation of separation of multicomponent gaseous mixtures across membranes is developed. It is shown that the governing differential equations for the plug flow geometries (crossflow, cocurrent flow, and countercurrent flow) are identical in form and can be reduced to a single general equation. The only difference lies in the manner the mole fraction of each component on the permeate side depends on its feed side composition at each point along the membrane. There are three important dimensionless factors, the pressure ratio, the permeabilities relative to that of the most permeable component, and either the stage cut or the dimensionless area, which describe the operation of the permeation unit. The method is equally amenable to cases for which the area is known and for which the stage cut is known. The separation of a binary mixture of N-2 and O-2 in all four flow geometries and of a mixture of H-2, CH4, CO, and CO2 in full mixing are simulated by the methods of thr present study, The results obtained are in good agreement with the values in the literature. The method is repeated for the simulation of separation of a mixture containing H-2, N-2, O-2, and CH4 for all four flow geometries.