Abstract: The liquid jet cutting machine contains at least one cutting head provided with an apparatus for producing high-pressure liquid at pressures in excess of 1000 bar. The cutting head delivers a high-pressure liquid cutting jet and is preferably movable or guideable along a predetermined cutting path. An apparatus is provided for holding the workpiece to be cut at least during the cutting operation. At least the high-pressure liquid producing apparatus, preferably inclusive of a drive and/or auxiliary aggregate, the cutting head, the holding apparatus and a cutting jet collector are connected with a common frame and form a positionally displaceable transport unit. The cutting head is preferably automatically controllable in its movements by a guiding apparatus which constitutes an industrial robot. The holding apparatus may also perform controllable movements and preferably contains an infeed and/or outfeed device for the workpiece to be cut, as well as a drain device for the spent jet liquid.