It is stated that the elements occurring in high-level nuclear reactor wastes can be safely immobilised by incorporating them within the crystal lattices of the constituent minerals of a synthetic rock (SYNROC). The preferred form of SYNROC can accept up to 20% of high level waste calcine to form dilute solid solutions. The constituent minerals, or close structural analogues, have survived in a wide range of geochemical environments for periods of 20 to 2,000 Myr whilst immobilising the same elements present in nuclear wastes. SYNROC is unaffected by leaching for 24 hours in pure water or 10 wt % NaCl solution at high temperatures and pressure whereas borosilicate glasses completely decompose in a few hours in much less severe hydrothermal conditions. The combination of these leaching results with the geological evidence of long-term stability indicates that SYNROC would be vastly superior to glass in its capacity to safely immobilise nuclear wastes, when buried in a suitable geological repository. A dense, compact, mechanically strong form of SYNROC suitable for geological disposal can be produced by a process as economical as that which incorporates radioactive waste in borosilicate glasses.