A high inner pressure type multistage compression rotary compressor having a support member blocking an opening of a cylinder constituting the rotary compression element and having a bearing of a rotary shaft. The surface of the support member on a side opposite to the cylinder is depressed, and a rib is added to a part of this depressed portion. A discharge muffling chamber formed in the surface of the support member on the side opposite to the cylinder is divided into a plurality of discharge muffling chambers, and the divided discharge muffling chambers are connected to each other by a passage disposed it a blocking plate and/or the rib.
