Abstract: Disclosed is a method for containing high-level radioactive waste in a body resistant to leaching by water. The method includes the steps of providing a mass containing radioactive substances and either a material which is resistant to leaching by water or a material which when heated forms a material resistant to leaching by water, enclosing the mass in a capsule, and then isostatically pressing the capsule at a temperature and pressure sufficient to form a coherent, dense body from the mass.