A canister apparatus, basket apparatus and combinations thereof for transporting and/or storing high level radioactive waste, such as spent nuclear fuel. In one embodiment, the invention can be a basket apparatus for supporting a plurality of spent nuclear fuel rods within a containment structure, the basket apparatus comprising a plurality of disk-like grates, each disk-like grate having a plurality of cells formed by a gridwork of beams; and means for supporting the disk-like grates in a spaced arrangement with respect to one another and so that the cells of the disk-like grates are aligned.