A laser beam machine has a laser head (3) for emitting a laser beam onto a workpiece which is to be treated, and a movement unit (1, 2, 9) for physically moving the laser head (3), which movement unit has a linearly moving machine portal (1) and a transverse carriage (2) which is held such that it can be moved on said machine portal in a transverse manner, wherein a flexible fiber cable (10) with a minimum permissible bending radius enters at an inlet point on the upper laser head end for transmitting the laser beam, and wherein a cable guidance system (12, 13) is provided in order to guide the fiber cable (10) at least over a portion of its length. In order to provide a laser beam machine proceeding from the above, in which laser beam machine inclined positions of the laser head (3) are also possible without the fiber cable (10) being subjected to excessive loading, the invention proposes that the cable guidance system (12, 13) has a deflection unit (13) which is fitted to the laser head (3) and which prespecifies a flexurally rigid deflection arc which extends above the inlet point and closely adjoins the inlet point, and by means of which deflection arc the fiber cable (10) is guided to the inlet point, and the radius of which deflection arc is greater than the minimum permissible bending radius of the fiber cable (10).