>>13109161Highly radioactive waste that puts out large amounts of thermal energy and therefore needs extensive shielding, and cooling, is classified as high level waste and only constitutes a small percentage to the total amount of radioactive waste.
In Germany for example, around 10% of all radioactive waste is High-level waste, but puts out 99.9% of the radiation.
Currently available Castor containers are rated to withstand an underwater pressure of 3 bar (20m depth) for eight hours and 20 bar (200m depth) for one hour.
Since these containers are ridiculously tough, they will likely withstand much higher forces, but not in terms of long term underwater storage.
To make underwater storage even remotely possible, you would have to transmute the waste first, reducing the time of storage from thousands to hundreds of years, though you would still need a secure underwater storage facility that is not influenced by currents, erosion ect. and provides necessary shielding.
Then you need containers of course which can withstand these high pressures for a long amount of time.
This would technically be possible even today, but it is still much more practical, cheaper and safer to store high level waste in currently available containers on land, even when we're talking long term.