This experimental study is conducted to determinestatistical models of surface roughness criteria inhard turning of high alloyed steel X38CrMoV5-1. Thissteel is hardened to 50 HRC, machined by a mixed ceramictool (insert CC650 of chemical composition70%Al2O3+30%TiC), free from tungsten on Cr-Mo-V basis,insensitive to temperature changes and having a highwear resistance. It is employed for the manufacture ofhighly stressed diecasting moulds and inserts with hightool life expectancy, plastic moulds subject to high stressand forging dies.Based on 33 full factorial design, a total of 27 testsare carried out. The range of each parameter is set at threedifferent levels, namely low, medium and high. Mathematicalmodels were deduced by the software Minitab(multiple regression method) in order to express the influencedegree of each cutting regime element on surfaceroughness. These models would be helpful in selectingcutting variables for the required surface roughness criteria.They can also be used for the optimization of hard cuttingprocess.The results indicate that feed rate is the dominantfactor affecting surface roughness, followed by cuttingspeed. As for the depth of cut, its effect is not very important.