An interesting study on the cutting of flexible steel using the CO2 laser is discussed in this paper. We used a rigorous mathematical model resulting from the experiments performed to determine the cutting speed, the deviation from the circularity of the disks, the geometry of the slit under more efficient conditions. I used a complete plan to make the cut. The focal position influences the cut, respectively the measured sizes. In the measurement process we used for Kerf the scanner and the electronic micrometer, and for the laser-cut surfaces the roughness meter and the durometer. The cutting process has been improved due to the use of the mathematical model. They were highlighted and calculated the cutting speed, the conicity due to the elliptical shape of the cut piece geometry when debiting the piece, conditions for minimizing the slit / cut channel. The relationships resulting from the part geometry indicate the circularity, data for the calculation of errors, the speed of work in stationary and dynamic piercing. The study is complex and varied because it can be supplemented with statistical data processing programs. The results of this article indicate the deviation from the circularity, the ellipse that approximates the piece, the composition of the speeds, the geometric modeling of the piece. All these relationships obtained accurately and accurately reproduce the dimensional accuracy of the pieces. By choosing the formulas expressed we can validate the calculation by comparing the measured values of the output parameters.