The present invention relates to at least: a spent nuclear fuel assembly container (1, 24, 26) provided with a metal cask (2) containing a spent nuclear fuel assembly, and a container body (3) substantially in the shape of a hexagonal tube and containing the metal cask (2); an assembly (18, 20, 22) of such spent nuclear fuel assembly containers (1, 24, 26); and a method of assembling the spent nuclear fuel assembly container (1, 24, 26).