Packaging for a plurality of medical containers comprising: • a nest comprising receiving openings (11, 12) for the containers, • a tub hereinafter referred to as the "first tub", adapted to removably receive said nest, said tub having: o a bottom wall, o first opposed lateral sloped walls (21b, 21b'), o second opposed lateral sloped walls (21a, 21a'), and o an upper opening with a peripheral flange, • a sealing cover placeable on said peripheral flange, each of said first and second opposed lateral sloped walls comprising at least one recess (35, 45) forming a supporting pillar (30, 40) on the inner side of said walls, with a supporting surface (31, 32, 41; 51) opposite to the bottom of the tub, said packaging being characterized in that: • a recess on each of the first opposed lateral walls (21b, 21b') forms a tub supporting pillar extending from the bottom of said tub up to the upper opening and comprising a tub supporting surface, • a recess (45, 55) on each of the first and second opposed lateral walls forms a nest supporting pillar (40, 50) comprising a nest supporting surface (32, 41, 51) extending below the tub supporting surface, and • the positioning of the recess forming a tub supporting pillar on one of the first opposed lateral walls is different from the positioning of the recess forming a tub supporting pillar on the other one of the first opposed lateral walls in order to allow the nesting of this first tub into a second identical tub when empty and when the first tub is in a first relative position with respect to the second tub, while allowing the stacking of said first and second tubs (6, 6') one onto the other when the first tub is in a second relative position with respect to the second tub, the bottom wall of the first tub being supported by the tub supporting surfaces of the second tub. • a nest comprising receiving openings (11, 12) for the containers, • a tub hereinafter referred to as the "first tub", adapted to removably receive said nest, said tub having: o a bottom wall, o first opposed lateral sloped walls (21b, 21b'), o second opposed lateral sloped walls (21a, 21a'), and o an upper opening with a peripheral flange, o a bottom wall, o first opposed lateral sloped walls (21b, 21b'), o second opposed lateral sloped walls (21a, 21a'), and o an upper opening with a peripheral flange, • a sealing cover placeable on said peripheral flange, • a recess on each of the first opposed lateral walls (21b, 21b') forms a tub supporting pillar extending from the bottom of said tub up to the upper opening and comprising a tub supporting surface, • a recess (45, 55) on each of the first and second opposed lateral walls forms a nest supporting pillar (40, 50) comprising a nest supporting surface (32, 41, 51) extending below the tub supporting surface, and • the positioning of the recess forming a tub supporting pillar on one of the first opposed lateral walls is different from the positioning of the recess forming a tub supporting pillar on the other one of the first opposed lateral walls in order to allow the nesting of this first tub into a second identical tub when empty and when the first tub is in a first relative position with respect to the second tub, while allowing the stacking of said first and second tubs (6, 6') one onto the other when the first tub is in a second relative position with respect to the second tub, the bottom wall of the first tub being supported by the tub supporting surfaces of the second tub.