The study on the roughness of Hardox cut laser parts is exploited in this article ranging from input parameters (laser power, pressure, cutting speed) to a Taguchi reduced to 9 references and then replicated under the same conditions 4 times. For the experiment, a fractional factorial plan L339 was chosen for three experimental parameters (P, v, p), each varied at 3 distinct levels. The blank used was HARDOX400 steel sheet with a thickness of 10 mm. This thickness is suitable for the study of several parameters that characterize the quality of laser cut parts: slot width, taperedness, flange roughness, dimensional precision. With the help of Statistica 7, the prediction and correlation formula of the influence factors were highlighted. DOE and SSM were used to obtain roughness while maintaining a constant parameter - laser power and simultaneously varying the pressure and cutting speed. It is found that pressure is a dominant influence factor.