IntroductionThe Inconel 718 is one of the most important materials used in modern industries. In addition of the best properties in terms of high strength, corrosion resistance, heat resistance and fatigue resistance, the Inconel 718 has, also a low thermal conductivity as it is mentioned by Lynch [1]. Certainly, this type of alloy is difficult to machine for the following reasons as it is presented by Alauddin [2]: High work hardening rates at machining, strain rates leading to high cutting forces; abrasiveness; toughness, gummy and strong tendency to weld to the tool with forming the built-up edge; low thermal properties leading to high cutting temperatures. However, it has a wide variety of applications such as aircraft gas turbines stack gas reheaters, reciprocating engines and others.In order to respond to the requirements of those applications, it is very important to forecasting surface roughness and cutting force. Consequently, it is necessary to search the best modeling approach of these output parameters. To obtain this objective, several approaches can be used as well as response surface methodology (RSM) and artificial neural network (ANN). Response surface methodology (RSM) is considered as a quick and useful procedure for the investigation and optimization of complex processes as well as modeling machining output parameters. Certainly, Davoodi and Eskandari [3] found that response surface methodology represents a better approach to predict tool life and productivity when turning of N-155 iron-nickel-base superalloy. Shihab et al. [4], investigated cutting temperature during hard turning of AISI 52100 alloy steel using multilayer coated carbide insert; they concluded that the developed RSM model is able to predict cutting temperature for different combination of input parameters very close to experimental values. Arokiadass et al. [5], used response surface methodology to modeling tool flank wear when end milling of LM 25 Al/SiCp with carbide tool. They concluded that the developed relationship can be effectively used to predict flank wear of carbide tool at a confidence level of 95%. Sahoo et al. [6], confirmed this conclusion when studying the development of flank wear model in turning hardened EN 24 steel with PVD TiN coated mixed ceramic insert under dry environment.