<p>Regenerative chatter and strong cutting vibrations frequently occur during the milling of flexible parts. Auxiliary fixtures have been employed to improve the stiffness of flexible workpieces, thereby suppressing chatter and vibrations. However, the influence of fixture parameters such as supporting forces on milling dynamics remain insufficiently understood, particularly for hydraulic fixtures. This study developed a hydraulic fixture with precisely controllable forces for thin-walled flexible workpieces. The milling process of flexible workpieces equipped with a hydraulic fixture was modelled by incorporating the effects of runout and vibrations. The dynamic responses were calculated employing a time-domain simulation algorithm, and stability characteristics were evaluated via stroboscopic sampling. The modal parameters of the flexible workpiece were obtained by varying the supporting forces of the hydraulic fixture, and the proposed model was used to predict chatter stability and cutting vibrations. A series of cutting experiments was conducted to validate the predicted stability diagrams and vibration displacements. Both the theoretical and experimental results demonstrate that the hydraulic fixture can significantly suppress regenerative chatter and cutting vibrations in flexible workpieces. Increasing the supporting forces enhances the dynamic stiffness of the flexible workpiece; however, this improvement gradually reaches saturation. Consequently, the suppression effectiveness of the regenerative chatter and cutting vibrations also reaches saturation. These findings provide quantitative guidance for the optimal fixture design and control of hydraulic fixtures in milling applications involving flexible components.</p>