A gasket integrated with a cover wherein a gasket material composed of a thermoplastic elastomer composition is integrally fixed to the cover having a shape of multistep contraction over at least two contraction steps, a gasket wherein the cover and the gasket are integrally molded and after molding, are subjected to a heating treatment at a temperature not lower than the temperature at which an adhesive component in materials constituting the gasket initiates crystal fusion or glass transition, or a gasket wherein the cover and the gasket are integrally molded and a covering layer composed of a fluoropolymer is formed on the gasket surface on atmospheric side are proposed. According to the present invention, a gasket integrated with a cover for a hard disc device which gasket is excellent in adhesive property and productivity, and is minimized in permeability and penetration of substances is provided.