A device for applying a sheet of covering material (4, 40) to boxes (1) having at least one wall (2, 200) with an outside surface (5, 50), an inside surface (6, 60) and a free edge (3, 30) intermediate between the surfaces (5, 6; 50, 60) comprises one or more elements (10, 100) for folding a flap (7, 70) of the sheet (4) around the intermediate edge (3, 30) so that the flap (7, 70) is made to cover the edge (3, 30) and then applying the flap (7, 70) to the inside surface (6, 60) of the wall (2, 200).