During the design of the machining technology, one of the important tasks is the choice of cutting modes, at the preliminary stage of the shaping process, which provide a given durability of replaceable cutting plates. In this case, when describing most of the design procedures of the machining process, there are problems associated with the algorithm for choosing the solution method and the response function at the appropriate processing stage. In this paper, as an algorithm for solving the problem, it is proposed to use the methodology of extreme planning of the experiment, which allows to obtain a mathematical model of the investigated multifactorial process. During the implementation of this algorithm in real production conditions, based on a priori information, the research area was selected and the levels of factors with intervals of their further variation in this area were established. Next, a factorial experiment was conducted and its results were processed on the basis of a linear polynomial that takes into account linear effects and interaction effects. As a result of checking the polynomial, a confidence interval was determined for all regression coefficients from three parallel experiments with the same values of factors. At the second stage, the adequacy of the mathematical model itself was evaluated according to the Fisher criterion. Finally, using the logarithm mechanism, a transition was made from the encoded values of the factors in the mathematical model to their natural values and a power function was obtained describing the effect of the cutting mode on the durability of a replaceable tungsten carbide carbide-based carbide plate. The conducted research makes it possible to speed up the procedure for assigning processing modes of workpieces at the preliminary stage in the conditions of existing production, to ensure a given tool durability, which allows to increase the productivity of the shaping process. This technique is the subject of consideration in this work.