This book aims to devise and establish quadratic regression equations including various input criterions of FSW technique to predict and determine the responses during the fabrication of AZ80A and AZ91C Mg alloy joints. The input process parameters taken into consideration include traversing speed of tool, speed of rotation of tool, its pin profile (geometry) and the axial force. A 5 level, 4-factor composite design (of central nature) was applied, and response surface methodology (RSM) was used to formulate quadratic regression models, to develop 3D response surface charts to anticipate the responses for various mechanical properties. Competency of the generated quadratic mathematical model was tested and validated using the technique of analysis of variance. Validation experimental trial results sketched in the form of scatter diagrams revealed precedent coincidence with that of the generated models. AZ80AMg alloy joints obtained using the tool having taper cylindrical pin geometry employed at 1045 rpm, 1.5 mm/sec traversing speed, under the exertion of an axial load of 4.87 kN, were found to exhibit improved mechanical properties.