Hanford, Washington- where much of the current waste is 'stored'.

A trench at Hanford in the 50s

"Until 1970, solid low-level and transuranic waste at the Atomic Energy Commission's nuclear weapons facilities (shown here is Hanford Reservation, circa 1950s) was frequently disposed of in cardboard boxes. Once filled, this unlined trench would have been covered with dirt, leaving the cardboard to deteriorate and allowing the waste to contaminate the soil and leach into the groundwater."

They STILL have leaking containers and areas where old waste has never been dealt with. They have not only the problem of where to store it, but of how to transport there and in what sort of containers.