We show a new approach, based on the utilization of Mathematica, to solve gas permeation problems using membranes. We start with the design of a membrane unit for the separation of a multicomponent mixture. The built-in Mathematica function, FindRoot, allows one to solve seven simultaneous equations instead of using the iterative approach of Professor Geankoplis. For this problem, the permeate and residue compositions as well as the membrane area are obtained. We also study the separation of air using membranes for each of the following cases: complete-mixing, cross-flow, countercurrent flow and co-current flow models. We show that membrane areas are within 10% of each other for all four cases. We find that the most efficient flow pattern is the countercurrent case followed by cross-flow and co-current flow, while the complete-mixing model gives the poorest performance. Finally, we plot the composition profile in both sides of the membrane module for the cross-flow case. The notebooks are available from the author upon request or at Wolfram Research.