A thermoplastic elastomer (“TPE”) which is oxygen-permeable is provided with excellent barrier properties against oxygen by melt-blending with a liquid polyisobutene oil plasticizer in an amount insufficient to render the plasticized elastomer tacky. If made tacky, enough detackifier is used to allow the product to be formed into a removable seal. The TPE may be a conventional thermoplastic vulcanizate or a block copolymer of a vinylaromatic compound, typically styrene, and a conjugated diene, typically butadiene or isoprene, or mixtures thereof; the block may be a diblock, triblock or higher block, but the preferred polyblock copolymer is a triblock with styrene end-blocks and a butadiene/isoprene mid-block. Preferably the diene mid-block is hydrogenated to provide a poly(lower)monoolefin mid-block. When the TPE is a TPV, some or all of the mineral oil used to make the TPV processable may also be substituted with the polyisobutene plasticizer. The elastomeric product is particularly useful for sealing elements for containers in which foods, beverages and medical products must be preserved for a long period.