The topic of the master’sthesis is mathematical modeling of the driving power in longitudinal turning. The first chapter briefly describes the problems faced by modern manufacturing companies and the importance of designing a technological process to overcome these problems. In the second chapter, turning processing is presented theoretically with an emphasis on the parameters of the technological process. The third chapter deals with the experimental part of the thesis. The central composite plan of experiments and the response surface method, which were applied in the rest of the thesis, are described in more detail. Also, the experiment carried out in the laboratory is described. In the fourth chapter, the statistical analysis of the experiments was carried out. Using the Design Expert program, variance analysis was performed and the associated linear and quadratic mathematical models were obtained. The results were tested on additional experimental data with graphical representation of both linear and quadratic models. In the fifth chapter, the optimization of the response surface from the previous chapter was carried out. The basics of optimization and the need for optimization of technological processes are theoretically described. Optimization methods, genetic algorithm and simulated annealing methods are also described. The Design Expert and MATLAB programs were used to determine the minimum and maximum values of the driving power. For both cases, the limit values inside and outside the area of the experimental space were considered (inside and outside the “cube” of the central composite plan of the experiment), and the obtained processing parameters were presented along with the corresponding value of the driving power.