The research deals with the optimisation of CNC turning process parameters to determine the optimal parametric combination that provides the minimal surface roughness (Ra) and maximal material removal rate. The experiment was conducted by the CNC turning process of S355J2 carbon steel. Data from the Taguchi design of experiments were the subject of analysis with Grey Relational Analysis (GRA) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). In the present study, three process parameters, such as cutting speed, feed rate and depth of cut, were chosen for the experimentation. It was found that 250 m/min cutting speed, 0.10 mm/rev feed rate and 1.8 mm depth of cut presented the optimal parametric combination by both used multi-objective optimisation methods. Analysis of variance (ANOVA) at a 95 % confidence level was used to determine the most significant parameters. Finally, the accuracy of GRA and TOPSIS results were validated by confirmation experiments.