The solubility of gaseous mixtures of CO2 and C2H6 in cross-linked poly(ethylene oxide) (XLPEO) has been modeled over a wide range of temperatures, pressures, and compositions with the Sanchez-Lacombe lattice fluid equation of state (LF EoS). The model binary gas-polymer parameters have been determined from pure gas solubility data and kept constant with temperature and composition. Multicomponent solubility is then calculated with no additional adjustable parameters, using a fully predictive procedure. The LF EoS model describes well the mixed gas solubility behavior data over wide ranges of temperature (from -20 to 35 degrees C), pressure (0-20 atm), and composition. The model also allows the representation of the solubility selectivity behavior of XLPEO at different conditions, permitting an a priori determination that ethane solubility is significantly enhanced by the presence of CO2, with a consequent reduction in CO2/C2H6 solubility selectivity relative to the pure gas value. In this regard, the behavior of this rubbery polymer is opposite that of many glassy systems, in which competitive sorption is often dominant, and the solubility of the less soluble gas (i.e., C2H6 in this case) is decreased by the presence of CO2, and the CO2 solubility selectivity is enhanced with respect to the pure gas value.