Abstract. The most important input quantities of waterjet cutting are the jet pressure, feed speed, stand-off distance, abrasive graining, mass flow, etc. Other quantities contributing to machining efficiency are the type of utilized abrasive or the tilt of the jet. Each of these quantities can be assigned different set points. The roughness of the machined surfaces and the thickness of the cut part are output quantities of the system, their values depending on the input parameters and the influence of various disturbing factors (noises). The paper discusses surface roughness obtained consequently to abrasive jet cutting. Optimisation of the machining system was achieved by intervening on five selected input quantities (factors), with two set points considered for each. Upon applying Taguchi methods, eventually the combination of factor set points was determined that ensures robust behaviour of the system.