This paper describes an experimental system for simultaneous permeation of a pressurized test gas through different gas permeable membranes and provides a proof of concept for a novel approach for gas identification/fingerprinting for potential construction of electronic noses. The design, construction, and use of a six-channel system which allows simultaneous gas permeation from a single pressurized gas compartment through six different parallel membranes are presented. The permeated gas is accumulated in confined spaces behind the respective membranes. The rate of gas pressure accumulation behind each membrane is recorded and used as a measure of the gas permeation rate through the membrane. The utilized gas permeable membranes include Teflon AF, silicone rubber, track-etch hydrophilic polycarbonate, track-etch hydrophobic polycarbonate, track-etch polyimide, nanoporous anodic aluminum oxide, zeolite ZSM-5, and zeolite NaY. An analogy between the rate of pressure accumulation of the permeating gas behind the membrane and the charging of an electric capacitor in a single series RC circuit is proposed and thoroughly validated. The simultaneous permeation rates through different membranes demonstrated a very promising potential as characteristic fingerprints for 10 test gases, that is, helium, neon, argon, hydrogen, nitrogen, carbon dioxide, methane, ethane, propane, and ethylene, which are selected as representative examples of mono-, di-, tri-, and polyatomic gases and to include some homologous series as well as to allow testing the potential of the proposed system to discriminate between closely related gases such as ethane and ethylene or carbon dioxide and propane which have almost identical molecular masses. Finally, a preliminary investigation of the possibility of applying the developed gas permeation system for semiquantitative analysis of the CO2-N2 binary mixture is also presented.