A tensioner (1; 50; 60) for a vehicle belt drive, having a housing (2) defining a cavity (3) having an axis (A); at least one arm (4) fitted to the housing (2) to rotate about the axis (A); an idle pulley (5) fitted to the arm (4); a torsion bar elastic member (6) housed at least partly in the cavity (3) and having a first end portion (15) integral with the arm (4), and a second hand portion (16) connected rigidly to a retaining portion (17) to permit tensioning of the elastic member (6); and a damping device (30) for damping oscillation of the arm (4), and having a conical friction member (32) cooperating axially with a mating surface (34) and loaded by axial elastic means (33). The friction member (32) is interposed between the arm (4) and the housing (2); and the elastic member (6) produces an axial thrust component depending on torsion of the elastic member and for pressing the friction member (32) and the mating surface.