Abstract: Machine for cutting strip-like material by a high pressure fluid jet comprising a substantially flat bearing surface able to support the strip-like material a cutting nozzle discharging a fluid jet under high pressure towards the strip-like material, means for displacing the nozzle in a direction Y perpendicular to the strip length, wherein it also comprises means for displacing the strip-like material in both senses according to a direction X parallel to the length of the strip, in such a way that the combined displacements of the strip-like material and the nozzle make it possible to make cuts of a random shape over a random length of the said strip-like material, wherein the bearing surface of the machine upstream of the cutting nozzle and on either side of the means for displacing the strip-like material, is in the form of a fixed table on which the latter moves within a guidance tunnel.