The influence of cutting parameters on surface roughness in face milling has been examined. Cutting speed, feed rate and depth of cut have been taken into consideration as the influential factors. A series of experiments have been carried out in accordance with a design of experiment (DOE). In order to obtain mathematical models that are able to predict surface roughness two different modeling approaches, namely regression analysis and neural networks, have been applied to experimentally determined data. Obtained results have been compared and neural network model gives better explanation of the observed physical system. Optimal cutting parameters have been found using simplex optimization algorithm.