a cutting machine for forming fracture lines in the cylindrical wall of plastic caps to facilitate the separation of a tamper - evident ring , including at least one cap support which rotates about an axis thereof and a laser beam emitter arranged , with respect to the support , so as to provide a laser beam that strikes the cylindrical wall of the cap , the emitter being activated and deactivated in accordance with the rotary motion of the cap , so as to form in the cylindrical wall of the cap a plurality of cuts alternated with short intact portions , which form a fracture line allowing the separation of the tamper - evident ring from the cup .