A finite element simulation of a gas permeation unit has been developed using COMSOL Multiphysics™ software. The simulation provides the solution to momentum and mass balance differential equations with appropriate boundary conditions and allows visualization of the velocity, pressure, and concentration profiles within the unit. Input to the model includes only physical properties from the literature, permeate and retentate operating pressures, and the inlet flow rate. Model predictions for permeate and retentate flow rates and compositions for both co- and counter- current flow configurations compare favorably with experimental results for a pilot scale Monsanto Prism™ membrane unit for air separation with hollow fiber polysulphone membranes. The solution-diffusion mechanism of separation is clearly illustrated using solubility and diffusivity data from the literature as model parameters. Important trends in the experimental results including (1) the permeate flow rate increasing with increasing pressure, but nearly independent of inlet flow rate, and (2) the permeate concentration increasing with increasing pressure and increasing inlet flow rate are correctly predicted by the model which is shown to have advantages over the simple algebraic well-mixed model and other gas permeation models in the literature.