This paper presents two-dimensional and three-dimensional transient numerical models of metal cutting. The simulations concern the study of the unsteady process of chip formation. These finite element models take into account dynamic effects, thermo-mechanical coupling with a rupture criterion and contact with friction. The yield stress takes into account the strain, the strain rate and the temperature in order to reflect realistic behavior in metal cutting. The rupture criterion adopted in the models presented here allows the definition of advanced simulations of the tool's penetration into the workpiece and of chip formation. The originality of such a criterion is that it is applied on all the workpiece and enables complex tool trajectories. Stress and temperature distributions, chip formation and tool forces are shown at different stages of the cutting process.