Abstract: A rack for storing spent nuclear fuel elements in which a plurality of aligned rows of upright enclosures of generally square cross-sectional areas contain vertically disposed spent fuel elements. Each fuel element is supported at the lower end thereof by a respective support that rests on the floor of the spent fuel pool for a nuclear power plant. An open rack frame is employed as an upright support for the enclosures containing the spent fuel elements. Legs at the lower corners of the frame rest on the floor of the pool to support the frame. In one exemplary embodiment, the support for the fuel element is in the form of a base on which a fuel element rests and the base is supported by legs. In another exemplary embodiment, each fuel element is supported on the pool floor by a self-adjusting support in the form of a base on which a fuel element rests and the base rests on a ball or swivel joint for self-alignment.