The invention concerns an assembly for packaging a volume of substance to be preserved by cryogenic vitrification characterized in that it comprises a sheathing (2) including a thin tube (6) having a predetermined internal diameter (Di) and a predetermined length (L); a support (3) comprising a zone for receiving said predetermined volume, said support (3) capable of being introduced inside said thin tube (6); and a plunger (4) for pushing forward said support (3), said support (3) then taking up a predetermined position in said thin tube (6) with an interval between each end (21, 22) of said support (2) and the neighbouring end (8, 9) of said thin tube (6).