Abstract: This invention concerns a machine for cutting pipes of different cross-section and diameter by means of a laser beam, comprising a laser source (26) and a system of mirrors for directing the laser beam from said source to a cutting head (7) for focalizing said beam on a pipe to be cut through a relevant mirror (Sp5, Sp7′). The cutting head is fitted rotating on an arm (3, 34) hinged on a bearing ring (5, 33) said bearing ring being on board a carriage (4, 32) sliding on a system of guide rails that can move parallel to the pipe to be cut.