Assembly formed by a tray for positioning elongated objects, in particular syringe bodies or syringes, and by these elongated objects, each of said elongated objects comprising a body and a flange (2b; 4), the tray including a plate with spaced apart openings (12a, 12b) intended to receive the bodies of the elongated objects and bearing surfaces (10, 13a, 16a) near said openings (12a, 12b) to receive the flanges (2b; 4) of these elongated objects when said bodies are engaged in said openings (12a, 12b); characterized in that: - the tray includes at least one first bearing surface (10, 16a) near a first opening, located at a first distance from the plate of the tray, and at least one second bearing surface near a second opening adjacent said first opening, located at a second distance from the plate of the tray, said second distance being different from said first distance; said first bearing surface does not coincide with the surface of the plate of the tray, being thus formed by a projection which the plate of the tray includes, and said projection is in the form of a tubular wall or chimney coaxial to said first opening; - said difference between said first and second distance is such that the flanges of the elongated objects are positioned at different heights from an opening to an adjacent opening, such that said flange (2b; 4) of the object engaged in one of these openings is able to rotate in this opening without contact with the flange (2b; 4) of the object engaged in the other of these openings; - said first and second openings (12a, 12b) are located at a distance one with respect to the other such that the flange (2b; 4) of the object engaged in one of these openings is able to partially overlap the flange (2b; 4) of the object engaged in the other of these openings, and - said difference between said first and second distance is such that said flange (2b; 4) of the object engaged in one of these openings is able to partially overlap the flange (2b; 4) of the object engaged in the other of these openings without contact with this flange (2b; 4). - the tray includes at least one first bearing surface (10, 16a) near a first opening, located at a first distance from the plate of the tray, and at least one second bearing surface near a second opening adjacent said first opening, located at a second distance from the plate of the tray, said second distance being different from said first distance; - said difference between said first and second distance is such that the flanges of the elongated objects are positioned at different heights from an opening to an adjacent opening, such that said flange (2b; 4) of the object engaged in one of these openings is able to rotate in this opening without contact with the flange (2b; 4) of the object engaged in the other of these openings; - said first and second openings (12a, 12b) are located at a distance one with respect to the other such that the flange (2b; 4) of the object engaged in one of these openings is able to partially overlap the flange (2b; 4) of the object engaged in the other of these openings, and - said difference between said first and second distance is such that said flange (2b; 4) of the object engaged in one of these openings is able to partially overlap the flange (2b; 4) of the object engaged in the other of these openings without contact with this flange (2b; 4).