This study presents a new method to determine multi-objective optimal cutting conditions and mathematic models for surface roughness (Ra and Rz) on a CNC turning. Firstly, cutting parameters namely, cutting speed, depth of cut, and feed rate are designed using the Taguchi method. The AISI 304 austenitic stainless workpiece is machined by a coated carbide insert under dry conditions. The influence of cutting speed, feed rate and depth of cut on the surface roughness is examined. Secondly, the model for the surface roughness, as a function of cutting parameters, is obtained using the response surface methodology (RSM). Finally, the adequacy of the developed mathematical model is proved by ANOVA. The results indicate that the feed rate is the dominant factor affecting surface roughness, which is minimized when the feed rate and depth of cut are set to the lowest level, while the cutting speed is set to the highest level. The percentages of error all fall within 1%, between the predicted values and the experimental values. This reveals that the prediction system established in this study produces satisfactory results, which are improved performance over other models in the literature. The enhanced method can be readily applied to different metal cutting processes with greater confidence. © 2012 Elsevier Ltd. All rights reserved.