When implementing a multi-variant design of the machining process, one of the important tasks is to select rational technological parameters at the final transitions of the shaping process that ensure the specified surface quality on the finished part made of the appropriate material. When modeling most of the design procedures at all stages of machining, there are problems associated with algorithmization of the solution method, adequate choice of the regression equation and the range of acceptable solutions at the specified processing stages. In this paper, as an algorithm for solving the problem, we propose the use of a well-known method of rational planning of the experiment, which allows us to obtain a mathematical model of the multi-factor process under study. In the process of implementing this algorithm, based on a priori information, the object of research was selected, its factors and the main levels of change of these factors were established. Next, a two-factor experiment plan was implemented using a numeric array from the well-known CoroKey catalog by SANDVIK Coromant. At the next step, the experimental data was processed using the existing method and on the basis of this information, private graphical dependencies of the studied parameter on the levels of factors were constructed. At the final stage, using the types of graphical dependencies, the regression equation of the investigated value of the cutting tool feed from two independent factors at three levels of each of them was formulated. To implement this algorithm, the least squares method was used, and the system of normal equations obtained on its basis. The proposed algorithm for obtaining the regression equation for solving problems in the field of machining production can be effectively used in computer-aided design systems for selecting technological parameters in the modes of processing parts with a blade tool, using numerical data from technological directories and atalogs of cutting tool manufacturers.