An elastic film, particularly for hygiene articles, has at least one layer that is produced extrusion of an elastomer polymer composition and subsequently cross-linked. The elastomer polymer composition contains a mixture of 40 to 90 parts by weight of a styrene block copolymer, 5 to 50 parts by weight of a plasticizer oil, and up to 10 parts by weight of a thermoplastic polymer. The layer of the elastomer polymer composition is cross-linked by treatment with electron beams. The elastomer polymer composition additionally contains 2 to 20 parts by weight of a reactive plasticizer that has a mole mass of less than 10,000 kg/kmol, is compatible with soft segments of the styrene block copolymer, and has functional acrylate groups.