The very limited waste isolation capacity of the host rock of mined repositories (MR), which is presently the most favored concept for disposal of high-level radioactive waste (HLW), requires use of engineered barriers in the form of metal canisters and clay seals. Requirements for the clay blocks are: sufficient expandability to maintain interconnectivity of mud, supercontainers, clay blocks and concrete, and sufficiently low creep potential of the clay blocks to prevent significant penetration and loss of expanded clay into rock fractures. Requirement for design of the mud and clay system for functioning over long periods of time in Ca-dominated salt water: the geotechnical properties of Ca-saturated clay components must be determined and assessed. Several coupled processes take place in the maturation of the buffer clay in MR and Very Deep Hole (VDH). They can be described in a strongly simplified form, assuming that the buffer blocks are homogeneous and completely occupy the deposition hole.