In this book, an attempt was put forward to formulate a Central Composite Design (i.e., CCD) based multi-objective numerical model using the technique of grey relational analysis, for optimizing the tool dependent parameters during the FSW of distinctive alloys of Mg namely AZ80A and AZ31B Mg, with the responses being the tensile strength and elongation percentage of the joints. Experimental works concentrating towards the sensitivity based analysis of the parameters during FSW of Mg alloys and their fine tuning related requirements for attaining superior quality Mg alloy joints have not been carried out so far. In this book, the objective based function was selected as the tensile strength of the attained AZ80A Mg alloy joints and 6 process parameters of the FSW (namely rotational speed of the tool, tool's traverse speed, force exerted axially downwards, shoulder & pin diameter of the employed tool and tool's hardness) were taken into consideration as the design related variables.