Nowadays, aluminum manufacturing companies are required to improve the manufacturing process of components with complex geometric details. This improvement requires an optimization of the process, resulting on higher cutting parameters. In thin floor parts, being low rigidity structures, the increase of cutting parameters brings as a conclusion the emergence of instabilities during machining.The main objective of this paper is to analyze the stability of thin floor parts, defining what cutting parameters make chatter appear and proposing one solution to instability problem based on Magnetorheological (MR) Fluid shock absorber.