A process for immobilizing high level radioactive waste (HLW) calcine comprises the steps of:(1) mixing the HLW calcine with a mixture of oxides, the oxides in the mixture and the relative proportions thereof being selected so as to form a mixture which, when heated and then cooled, crystallizes to produce a mineral assemblage containing well-formed crystals capable of providing lattice sites in which elements of the HLW are securely bound, the crystals belonging to or possessing crystal structures closely related to crystals belonging to mineral classes which are resistant to leaching and alteration in appropriate geological environments and including crystals belonging to the titanate classes of minerals; and(2) heating and then cooling the mixture so as to cause crystallization of the mixture to a mineral assemblage having the elements of the HLW incorporated as solid solutions within the crystals thereof.A mineral assemblage having elements of HLW calcine incorporated within the crystals thereof is also disclosed.