A laser processing machine for processing workpieces, in particular metal sheets, includes a workpiece support and a beam receiver for the laser beam used as a processing tool. The distance between a workpiece lying on the workpiece support and the beam receiver is variable, owing to the fact that the workpiece support and the beam receiver are positionable relative to one another along the beam axis of the laser beam by means of an adjusting drive of an adjusting device with a positioning movement of a variably definable magnitude. A method for processing workpieces, in particular metal sheets, is also provided.