Abstract: Waste material such as toxic compounds, radioactive waste materials and spent nuclear fuel rods are encapsulated in a container system which is subjected to a hot pressure process to cause a protective powder material located around the waste material to form a dense matrix and function as a highly corrosion resistant and protective shroud. Embodiments include hot isostatic pressing and hot uniaxial pressing, the use of metal powder such as copper powder for the protective powder material or alternatively ceramic powder and, depending upon the embodiment chosen, the use of a single container or dual container system in which a first container is located within an outer container. Either or both of such containers may be cylindrical with a bellows-like side wall to facilitate compression thereof in an axial direction.