A 3D finite element model of the machining of Ti6Al4V alloy has been developed. This model is able to simulate the formation of continuous or discontinuous chips during the cutting process that depends on the cutting conditions. In this model, the yield stress is considered as a function of the strain, the strain rate and the temperature. The dynamic effects, thermo-mechanical coupling, constitutive damage law and contact friction are taken into account. The stresses and temperature fields, chip formation and tool forces are obtained at different stages of the cutting process.