The article presents original technological methods that allow the improvement of the accuracy of the turning and grinding of elastic-deformable shafts by increasing their stiffness by controlling the state of elastic deformations. In particular, the adaptive control algorithm of the machining process that allows the elimination of the influence of the cutting force vibration and compensates for the bending vibrations is proposed. Moreover, a novel technological system, equipped with the mechanism enabling the regulation of the stiffness and dedicated software, is presented. The conducted experimental studies of the proposed methods show that, in comparison with the passive compliance equalization, the linearization control ensures a two-fold increase in the shape accuracy. Compared to the uncontrolled grinding process of shafts with low stiffness, the programmable compliance control increases the accuracy of the shape by four times. A further increase in the accuracy of the shape while automating the processes of abrasive machining is associated with the proposed adaptive control algorithm. Moreover, the initial experiments with the adaptive devices prove that it is possible to reduce the longitudinal shape inaccuracy even by seven times.