Three molecular simulation techniques to predict the gas sorption isotherms in a glassy polymer membrane in contact with a single- or a mixed-gas reservoir have been tested on a large-scale ~50000 atom 6FDA-6FpDA polyimide bulk model over a wide range of pressures. Both single- and mixed-gas uptake curves were obtained for CH4, N2 and CO2 over the 0–60 bar range using either a Grand Canonical Monte Carlo (GCMC), an iterative test particle insertion - molecular dynamics (TPI-MD) or an iterative GCMC-MD method. Virtual TPI and actual GCMC insertions of gas molecules into the polymer matrices were performed using the excluded-volume map sampling approach (EVMS), which improved the sampling efficiencies by a factor of ~10–20 over random insertions.The simulation techniques were first used to obtain the single-gas sorption isotherms and the associated ideal gas sorption selectivities. The TPI-MD and GCMC-MD approaches gave consistent results in agreement with experiment. Further tests were made on a binary 2:1 CH4/N2 and a ternary 16:8:1 CH4/N2/CO2 gas mixture in equilibrium with the 6FDA-6FpDA model matrix. For such mixed-gas feeds, the uptake of each gas in the polymer depends on its gas phase concentration and on its solubility in both the gas mixture and the polymer phases. Solubilities of penetrants in the polymer phase correlated well to the total penetrant concentration. In the binary mixture, the sorption of N2 was strongly hindered by that of CH4. In the ternary mixture, the introduction of the highly-soluble CO2 at a relatively low partial pressure significantly reduced the sorption of both CH4 and N2, although its concentration was insufficient to plasticize the polymer. As such, the mixed-gas CH4/N2, CO2/CH4 and CO2/N2 sorption selectivities were found to differ from their ideal values. Interference effects were characterized by a novel technique which estimates the proportions of molecules of each type of penetrant excluded by competitive sorption for the mixtures under study.The main asset of such iterative molecular simulations is their ability to take implicitly into account the interdependence of the different gas concentrations and solubilities as well as the associated changes in the matrices over a large range of pressures and temperatures. In addition, the iterative GCMC-MD method should be applicable to even more complex mixtures, which is obviously pertinent with respect to industrial gas separation applications.