This packaging is for containers having each a cylindrical body and a upper surface located at or near an extremity of the body, said packaging (1) comprising a nest (5), a tub and a sealing cover the nest (5) comprising at least one first supporting surface (18), to be received on at least one corresponding supporting surface (26) of the tub (6), the tub (6) having a bottom wall (20), lateral walls (21) forming an upper opening (22), and a peripheral flange (23) levelled with said upper opening (22), for the sealing of said sealing cover thereon, According to the invention, said nest (5) comprises at least one second supporting surface (17a) rigidly connected to said at least one first supporting surface and so positioned with respect to this at least one first supporting surface that this second supporting surface (17a) is located, when the nest (5) is placed in the tub (6), at the level of said peripheral flange (23).
