The invention relates to a package comprising a packaging for storing and/or transporting radioactive materials and an assembly containing radioactive materials (16) housed in a cavity of the packaging closed by a cover (6), the package comprising a system for dampening impact of the assembly against the cover (6), the system comprising at least one deformable dampening device (42) and a loading device (26) of the deformable dampening device. According to the invention, one of the devices (42) is mounted moveable on the cover (6) in a plane orthogonal to the axis (8) of the packaging, and has means (50) of self-centering relatively to the other of the devices (26), provided on the assembly containing the radioactive materials (16).