► The surface roughness is measured during turning at different cutting parameters such as speed, feed, and depth of cut by full factorial experimental design. ► Artificial neural networks (ANN) and multiple regression approaches are used to model the surface roughness of AISI 1040 steel. ► The ANN model estimates the surface roughness with high accuracy compared to the multiple regression model. Machine parts during their useful life are significantly influenced by surface roughness quality. The machining process is more complex, and therefore, it is very hard to develop a comprehensive model involving all cutting parameters. In this study, the surface roughness is measured during turning at different cutting parameters such as speed, feed, and depth of cut. Full factorial experimental design is implemented to increase the confidence limit and reliability of the experimental data. Artificial neural networks (ANN) and multiple regression approaches are used to model the surface roughness of AISI 1040 steel. Multiple regression and neural network-based models are compared using statistical methods. It is clearly seen that the proposed models are capable of prediction of the surface roughness. The ANN model estimates the surface roughness with high accuracy compared to the multiple regression model.