The paper presents an analysis of the possibility of increasing the accuracy and stability of machining of low-rigidity shafts while ensuring high efficiency and economy of their machining. An effective way of improving the accuracy of machining of shafts is increasing their rigidity as a result of oriented change of the elastic-deformable state through the application of a tensile force which, combined with the machining force, forms longitudinal-lateral strains. The paper also presents mathematical models describing the changes of the elastic-deformable state resulting from the application of the tensile force. It presents the results of experimental studies on the deformation of elastic low-rigidity shafts, performed on a special test stand developed on the basis of a lathe. An estimation was made of the effectiveness of the method of control of the elastic-deformable state with the use, as the regulating effects, the tensile force and eccentricity. It was demonstrated that controlling the two parameters: tensile force and eccentricity, one can improve the accuracy of machining, and thus achieve a theoretically assumed level of accuracy.