A numerical analysis was performed for the optimal design of a multiple stage membrane process to separate carbon dioxide from its mixture of nitrogen. The nonlinear ordinary differential equations were simultaneously solved using a finite difference method. The permeance of carbon dioxide and its selectivity were obtained from the experimental separation data using the numerical analysis as a function of both the mole fraction of carbon dioxide and the feed pressure in the gas mixture. The numerical analysis results showed that the pressure ratio of the permeate side to the feed side was a quite important factor since it affects both the carbon dioxide concentration in the final permeate and the membrane area required for the 90% recovery of carbon dioxide and the concentration of 99% carbon dioxide in the final product.