This paper is aimed at analyzing the results of a friction welding experiment, in English friction stir welding (FSW), and to describe an optimized and representative model of the output variables according to each input variable of the welding process. The determination of the best combination of input parameters guarantees the good quality of the weld, meeting the technical specifications of the process. This was possible through the use of the response surface methodology, widely used in the industrial and research fields, when processes involving more than one input variable, demand high quality and reliability of the results. To estimate the most appropriate second-order model, a genetic algorithm was used to search for the optimal solution, which is a more robust alternative in terms of meeting the global minimum. The development was based on the use of MATLAB, version R2020b, where the model equations were estimated, and the surface and contour graphics were constructed. The validation of the modeling and optimization went through the use of analysis of variance (ANOVA), and the determination coefficient (R2), the regression and residue graphs were also verified. The results showed interesting behaviors related to the combination of input variables - tool rotation and welding speed - especially when analyzed at the beginning of the process and along the entire welding path. After estimating the models for the tool s input and path responses, it was possible to superimpose the contour curves and analyze in which regions the maximum mechanical stress occurred. In this way, we can indicate how the intensity of rotation and speed influence each step, which makes it possible to determine the best working range for each phase of the welding process, reducing the effects of the resulting forces. This is important to avoid premature tool wear, increase efficiency and to control weld quality parameters.