Abstract This experimental investigation aims to formulate quadratic regression based empirical model taking into account the parameters of friction stir welding (FSW) process for predicting the optimized process parameters to maximize the response (i.e., ultimate tensile strength) of the distinctive alloys of Mg joints. Parameters of FSW process taken into consideration includes tool’s traverse speed, axial force and rotational speed of tool and response being the fabricated joint’s tensile strength. A central composite rotatable category 3–factor, 5 level design based matrix was formulated and response surface methodology was used to obtain regression based models, to generate contour plots and to visualize the interactive impacts of parameters on the joint’s tensile strength. Formulated quadratic regression based model was validated employing analysis of variance. Comparison amidst the realistic and anticipated values of the response announced the superior fitting accuracy of the formulated quadratic model. For a constant tool’s rotational speed (of 1000 rpm to 1250 rpm), the tensile strength was observed to be highly sensitive to the axial force values than the tool traverse speed values. Mean tensile strength of the friction stir welded AZ31B, AZ80A, AZ91C, AM50A and ZK51A-T5 Mg joints during the employment of optimized process parameters were found to be 217.5 MPa, 251.4 MPa, 231.9 MPa, 192.1 MPa and 173.2 MPa respectively, thereby exhibiting perfect agreement with the anticipated values.