An apparatus is provided for cutting pieces from laminar material wound in coil using a laser or plasma cutting machine. In one apparatus according to the invention, a cutting station includes at least one moveable cutting head arranged between the station's entrance and exit, and a means to position a portion of laminar material on a cutting plane. The positioning means includes three separate locking devices, each of which can lock on a portion of the laminar material as it passes through the cutting station. The three locking devices are arranged in succession: the first near the cutting station's entrance, the second near the exit, and the third between the first and second locking devices. At least the third locking device is movable, in the space between the other two devices, along a portion of laminar material while the material is kept under tension.