An endeavour was put forward to friction stir weld flat plates of AZ80A Mg alloy by employing the central composite based design technique of response surface methodology, taking into consideration the parameters namely tool rotational speed, traverse speed, tool’s tilt angle, and pin geometry of the employed tool. Numerical model was formulated to correlate the relationship amidst the employed parameters of FSW process and the responses, namely tensile strength and elongation percentage of the AZ80A Mg alloy joints. The formulated model was also optimized to attain AZ80A Mg alloy joints possessing highest value of tensile strength. Competency of the formulated numerical model was validated employing the analysis of variance and the observations of the affirmation experiments plotted in the form of scatter diagrams revealed an appreciable agreement with the values of the anticipated models. Response and contour plots generated from the established numerical model was employed to understand the interactive impacts of the parameters of FSW process on the variables of the response. AZ80A mg alloy joints fabricated during the employment of tool possessing straight cylindrical geometry at atilt angle of 0.630, rotational speed of 962.077 rpm, tool traverse speed of 2.105 mm sec−1 possessed the highest tensile strength of 195.299 MPa and was proven to be free from flaws.