The thermodynamic changes that accompany mixed gas sorption in glassy polymeric materials are examined. The solid polymer is treated as an elastic solid in the analysis. Two contributions are identified : deformation of the solid to accommodate the penetrant and mixing of the deformed solid and penetrant. Equating the chemical potential of the penetrant in the gas phase to that in the solid yields sorption isotherms. By estimating two material parameters, the penetrant partial molar volume and interaction parameter, from pure gas sorption measurements, a priori predictions of mixed gas sorption are possible. The resulting sorption isotherms are compared to two sets of experimental measurements : carbon dioxide, ethylene, methane and nitrous oxide sorption in poly(methyl methacrylate) and carbon dioxide and methane sorption in poly(phenylene oxide) and carboxylated poly(phenylene oxide). The predicted mixed gas sorption isotherms are in good agreement with experimental data.