There is provided a rotary compressor comprising an electric element, and first and second rotary compression elements driven by the electric element, these components being provided in a hermetically sealed container, CO 2 refrigerant gas compressed by the first rotary compression element being discharged into the hermetically sealed container, and the discharged refrigerant gas of intermediate pressure being further compressed by the second rotary compression element, a cylinder constituting each rotary compression element, a support member adapted to seal an opening surface of each cylinder, and provided with a bearing of a rotary shaft erected on a centre, a discharge muffler chamber formed in the support member outside the bearing, and communicated with an inside of the cylinder and a cover attached to the support member to seal an opening of the discharge muffler chamber, wherein each cylinder, each support member and each cover are fastened by a plurality of main bolts, and each cylinder and each support member are fastened by auxiliary bolts located outside the main bolts.