[en] One proposal for disposing of radioactive waste is to put it in drill holes or mined cavities so deep that the waste would be effectively isolated from the surface. Even if radioisotopes escaped from the disposal canister, they would be removed from the circulating groundwater system by sorption and/or chemical reaction in their transit on very long paths to the surface. This report summarizes the feasibilities and costs of making deep holes and deep mine shafts; estimates probable technological advances by the year 2000; presents thermal history and thermally induced stress calculations based on several assumptions regarding age of waste and density of emplacement; and summarizes lack of knowledge that bear upon the isolation of waste at great depth. In strong rock, present technology would probably enable us to drill a hole 20 cm in diameter to a depth of 11 km and sink a shaft 10 m in diameter to about 4.4 km. By the year 2000, with advancement of technology, holes of 15 km depth and 20 cm diameter could be drilled, and shafts of 6.4 km or deeper could be sunk. The heat output of 5.5-year-old spent fuel and 6.5-year-old reprocessed waste is used to calculate temperature increases and stress buildings in the surrounding rocks. Some waste configurations may cause unacceptably high temperature increases; indeed, limitations on temperatures reached will in some cases limit the packing density of waste canisters and/or require longer cooling of the waste before emplacement. Sealing boreholes and shafts for significant times, i.e. 1,000 to 100,000 years presents additional problems. The casing or ling of the borehole or shaft would have to be removed in the region where seals are constructed, or the lining material would have to be designed to function as an integral part of the long-term seal. Sealing fractures in the rock around the borehole or shaft will be quite important