Turning on semi-automatic lathes with multiple knives is a frequent practice in the engineering works, in order to lower the working time and price cost of the cutting process. Turning on multiple-tool holder is efficient only in the conditions of optimum cutting rate and number of tools. The classical calculation of the cutting rate and tool number requires a great volume (quantity) of work and doesn't assure optimum results, as it is based on prescribed (imposed) values of some variables of the cutting process. These shortcomings of the classical calculation are eliminated by using the convex mathematical programming theory in order to draw-up a mathematical model that could be solved rapidly with the aid of a computer on the basis of a known algorithm. Certainly, the results will be the optimum ones. The optimization function of the mathematical model have been considered to be the expression of the cost price of multiple cutting and the restrictive functions are just those prescribed (imposed) for the cutting process. Our paper presents the determination of the optimization function for turning a straight axle (shaft pri, spindle) and an axle in steps, the restrictive functions which limit the cutting rate and the optimum tool number, and the respective mathematical models. The block diagram of the Kelley algorithm is also presented. It helps to develop the program for the resolution of the mathematical model with the aid of the computer.