Abstract: A method of disposing of radioactive waste comprising the steps of: providing a pressure-equalizing container; filling the pressure-equalizing container with radioactive waste; and burying the waste filled container in a subduction fault region of the earth's crust. For a preferred embodiment of the process, the waste filled containers are buried in the mud on the ocean floor in a subduction fault region. Preferably, the containers are placed on the ocean side of the fault, rather than the continental shelf side. The pressure-equalizing container is preferably fabricated from stainless steel, with a lead seal, although containers fabricated from ceramic materials may also be used. The waste-filled containers are transported by ship to the area above a subduction fault, and an unpressurized, remote-controlled “submarine crawler” takes a number of containers to the ocean floor and buries them there, individually, in the mud or sediments.