The paper considers the impact of weight and cutting forces on deflection and pressing of the non-rigid part — propeller shaft. The analysis of literature sources in the field of kinematics and dynamics of the process of turning by the cup tools was conducted.The purpose of the work was stated as a result of the analysis. The purpose of this paper is to derive a mathematical expression of the dependence of deflection and pressing values of the non-rigid shaft on its own weight and cutting forces.The propeller shaft of the mine pump was selected as the object of research. The design of the propeller shaft is characterized as non-rigid. Therefore, it was the object of further researches.To derive the mathematical expression of shaft deflection under its own weight, the weight was considered as a uniformly distributed load.Differential equation of Euler-Bernoulli was used in order to solve this problem. In the process of turning, round tool under the influence of feed moves along the workpiece and presses on it in every particular point. The Vereshchagin’s method was used to derive the mathematical expression of shaft deflection from the cutting force.The results obtained in this work can be applied to the process of turning of all non-rigid shafts by the round cup tool.The mathematical expressions of deflection of the propeller shaft under its own weight and its pressing by the cutting forces allow optimizing the process of turning and improving the accuracy and quality of processing.