The paper presents a design concept for an underwater drilling rig which can operate up to a depth of 5000 m below sea level. The proposed main hull of the drilling rig is in the form of a thick-walled toroidal shell, although other possible forms are considered. The proposed primary method of power generation is via a pressurised water nuclear reactor. Considerations are made as to the health and safety of the crew and also to the transport of the retrieved oil.