Abstract: A pressure vessel including a cylindrical vessel shell body, a bottom, and a cover, which are composed of cast elements and are clamped together or restrained by axial prestressing tendons located in channels which are distributed over the periphery of the cylindrical shell body, have axes which are parallel to the axis of the vessel, and by tangential prestressing cables located in annular channels on the outer surface of the vessel. The pressure tank also includes a steel liner which is anchored by means of a special gun welded or bolt connection directly to the inner side of the tank shell body. This tank shell body includes at least two cylindrical shells which are formed of cast elements and are successively arranged when viewed in the radial direction.