Cross-linked rubbery polyurethane-ether polymeric membranes are made from cross-linked rubbery polyurethane-ether polymers that are synthesized from a diisocyanate-terminated polyether and a tetrol with four hydroxyl functional groups. The hydroxyl groups on the tetrol react with the isocyanate groups on the diisocyanate-terminated polyether to form urethane bonds. The cross-linked rubbery polyurethane-ether polymeric membrane selectively permeate condensable vapors such as C3 to C35 hydrocarbons, aromatics, water vapor, carbon dioxide, and hydrogen sulfide and rejects methane and ethane. The cross-linked rubbery polyurethane-ether polymeric membrane have high permeance for condensable vapors, high selectivity for condensable vapors over methane and ethane, and high resistance to liquid chemicals.