This article investigates the vibration cutting process of Ti6Al4V alloy numerically and theoretically. The Coupling Eulerian-Lagrangian finite element models with one-tool and double-tool are established, to simulate the cutting processes with tool forced vibration and self-exited vibration respectively. It is shown that low-frequency forced vibration aggravates the periodic shear banding instability and increases the cutting force amplitude, whereas high-frequency forced vibration can improve the machined quality. Furthermore, the self-exited vibration due to fluctuating cutting thickness with low frequency promotes the shear banding evolution in chip. The self-exited vibration stability limit is found dependent on the frictional behavior, penetration resistance and the inherent vibration sources of tool-workpiece system. These simulation results show good agreement with theoretical models, which provide practical guidelines for improving vibration machining. © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of The 17th CIRP Conference on Modelling of Machining Operations