To provide a composition excellent in gas barrier property, hygienic property, compression set, vibration-damping property, and fluidity in molding, and to provide a medicinal tap, a beverage cap liner and a damping material, using the composition.

The composition comprises a thermoplastic elastomer (E) and 5-100 pts.wt. polypropylene-based resin (F), wherein 100 pts.wt. isobutylene-based polymer (A) having alkenyl at its terminal end is melt-kneaded with 10-300 pts.wt. polypropylene-based resin (B) and/or isobutylene-based block copolymer (C) comprising a polymer block (a) composed mainly of an aromatic vinyl-based compound and an isobutylene-based polymer block (b) and is dynamically crosslinked by a hydrosilyl-containing compound (D) to obtain the thermoplastic elastomer (E), and the polypropylene-based resin (F) has 40 g/10min melt flow rate of 230C and 2.16 kg load.