A support element for a plurality of packaging straws, the support element comprising a plate (31) and two flanges (37) rigidly connected to said plate (31) and comprising a fluted surface (53) having a plurality of similar grooves (36), each flange (37) comprising a central part as well as a first projecting part (42) and a second projecting part (43), each extending from one side of the central part, characterised in that the first projecting part comprises a bracket (42) having a bearing face and the second projecting part comprises another bracket (43) having another bearing face, said bearing face and said other bearing face being upwards facing and, in the direction of height, said bearing face being further from said plate (31) than said other bearing face. The assembly comprises the support element and a freezing rack (4).