Salt
Beds of salt up to 1 kilometre thick lie within 1 or 2 kilometres of the surface across much of the US. They were deposited hundreds of millions of years ago by evaporating seas.
Room-temperature radioactive waste from the production of nuclear weapons has already been stored in one salt deposit - in the Waste Isolation Pilot Plant near Carlsbad, New Mexico, since 1999. Now the US and Germany are considering salt for future waste repositories.
Pros: Salt can flow like slow-moving Silly Putty - so any fissures seal themselves. Buried waste would relatively quickly become encapsulated by the salt, which would close in around it due to pressure from surrounding rock.
Cons: The still-hot waste could cause small amounts of water trapped in the salt around it to move, carrying with it radioactive materials. Read the full report here.
Source: New Scientist.