At least one irradiated product, such as a fuel assembly (1), is introduced into a metallic container (4) delimiting a chamber whose cross section is adapted to accommodate the cross section of a (single) product such as a fuel assembly (1). A neutral gas is introduced into the chamber of the container (4) and the chamber is sealed in tightly in such a way that the neutral gas cannot escape. The container (4) with the fuel assembly (1) is placed in a channel (10) of a storage facility, the container (4) and the fuel assembly (1) being positioned horizontally. Cooling air (25) which is in contact with the outer surface of the channel is circulated (10). Contamination inside the channel (10) can be monitored continually in a space (31) surrounding the container (4).