A rubber material is described, modified with a barrier material in the form of a copolymer which can be produced via ring-opening metathesis polymerization of a) at least one olefin monomer selected from the group consisting of monocyclic olefin monomers having one or two endocyclic C—C double bonds and bicyclic olefin monomers having one endocyclic C—C double bond and b) at least one polycyclic olefin monomer having at least two C—C double bonds. The barrier material can be used to reduce the gas permeability of the rubber material.