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SummaryBlanking and machining are commonly used in processes to obtain the shape of many mechanical pieces. Although considerable number of experimental results exist, certain essential aspects of cutting are still not well understood. This comes from the complexity of the thermomechanical phenomena induced by the material separation as well as from the complexity of the dynamical behaviour of the whole workpiece/tool/machine system. Numerical simulations make it possible to go further in the comprehension and the prediction of machining and cutting processes. In this work the state-of-the art is analysed and we present the most recent developments in the contribution of computational mechanics to numerical simulation of machining and blanking. This contribution is, on one hand, developed at a very global scale called macroscopic scale. At this scale a representation of the deformations of the piece is necessary, for example when thin walls are present, and when both predictions of the geometrical state of final surface and/or stability of the process are expected. On the other hand, the contribution is also located at a more local scale: the mesoscopic scale. At this scale, the aim is the determination of thermomechanical sollicitations applied to the tool, the simulation of chip formation, or the description of residual states (mechanical, chemical) inside the workpiece after machining.