The Arbitrary Lagrangian Eulerian approach (ALE) presents a lot of advantages. However, its use is limited to the cutting with a constant uncut chip thickness h. On the one hand, the previous numerical studies were focused on the prediction of the quasi-stationary response for cutting forces and heat transfer along the tool rake face. But on the other hand, in the industrial machining processes, as milling operations, the removal of the material from the workpiece varies with time. The aim of the present work is to extend the use of the ALE approach to the milling processes where the cutting conditions are transient: h varies with time. A new strategy combining the ALE approach and the tool translation is presented. In the present model, the out flow surface of the chip is assimilated to an Eulerian surface with a vertical moving direction of the mesh. This strategy allows to consider the increase of the tool-chip contact length with h as in up milling. The limitations of the conventional use of the ALE were also discussed in this study. The experimental study was focused on dry machining of the aluminum alloy AA2024–T351 at very high speed 51.5 and 66.2 m/s. The predicted cutting forces have been compared with the experimental results. The cutting forces are not proportional to h especially for the feed force. This tendency, reproduced by the model, is directly related to the thermal softening of the work material in the secondary shear zone. At the tool rake face, the variation of the local parameters in function of time is also discussed: tool-chip contact length, sticking zone and temperature.