Friction Stir Welding (FSW) is a solid state welding which uses non-consumable steel rod to weld two materials. Friction stir welding is an emerging process which is based on frictional heat generated through contact between a non-consumable rotating tool and work piece. Friction stir welding technique possesses several advantages over other conventional types of welding due to the fact that process is carried out in solid state. Removal of melting helps in minimizing porosity and eliminates oxide inclusion. In this study, we focus on the optimization of the process parameters in friction stir welding of two different aluminium alloys (6061, 7075) using Taguchi method of experimental design. Al 6061 and Al 7075 are the two different alloys of aluminium. Among these Al 7075 has mechanical properties nearly double than that of Al 6061, but Al 6061 is used more extensively than Al 7075 because of its low cost. Al 6061 and Al 7075 being alloys of aluminium varies in the composition of alloying elements used in their manufacturing. Al 6061 has magnesium and silicon as its major alloying elements whereas Al 7075 has zinc as its primary alloying element. Al 6061 comes with medium to high strength, exhibit good toughness and surface finish, excellent resistance to corrosion at environmental conditions and another important property is its good weldability. Al 7075 being stronger than Al 6061 lacks in its resistance to corrosion and has poor weldability. Al 6061 is readily weldable but Al 7075 is not, because it is prone to micro-cracking during welding. This study also describes the relation between process parameters and their response of friction stir weld on ultimate tensile strength and hardness of composite materials using mathematical models. The process parameters considered are rotational speed, welding speed and number of passes. Different methodologies are used to develop the models to predict the responses and mechanical properties such as ultimate tensile strength and hardness. The objective of Multiple Regression Analysis (MRA) is to construct a model that explains as much as possible, the variability in a dependent variable, using several independent variables. Group Method of data Handling Technique (GMDH) is a family of inductive algorithms for computer-based mathematical modelling of multi-parametric datasets that features fully automatic structural and parametric optimization of models. GMDH is used in such fields as data mining, knowledge discovery, prediction, complex systems modelling, optimization and pattern recognition. As the machining process is non-linear and time dependent, it is difficult for the traditional identification methods to provide an accurate model. Compared to traditional computing methods, the Artificial Neural Network’s (ANN) are robust and global. Estimation and comparison of machining responses were carried out by MRA, GMDH and ANN.