Disposal of canisters with Highly Radioactive Waste (HLW) in boreholes in crystalline rock can be made by use of “supercontainers” with waste and clay seals, moved down in clay mud which undergoes consolidation under the swelling pressure exerted by the dense clay seals. The concept can be used for disposal in mined repositories at a few hundred meters depth and in very deep boreholes (VDH) with saline, stagnant formational waters that are unlikely to rise to contaminate shallow groundwater. For disposal in mined repositories the supercontainers are suitably placed in 8-10m long inclined boreholes with 1,900mm diameter. The concept for disposal of HLW in the lower halves of 4 km deep holes relies primarily on the sealing capacity of engineered barriers, clay and concrete, in the upper halves of the holes. The parts of a VDH that are located in fracture-poor rock are sealed with dense, expandable clay, and by concrete cast where pre-grouted fracture zones are intersected. The deep holes will undergo convergence and eventually expose the clay, concrete and waste packages to radial compression. Using the Kelvin rheological model for predicting the radial convergence of the holes these components will be subject to a small pressure increase in the first 10,000 years. In a longer time perspective, they will be compressed by the slowly increasing confining pressure causing improved sealing ability of the clay.