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Metallic parts for the aeronautics industry are usually manufactured by material subtraction using machining processes. The gradual relaxation of the bulk material residual stresses during machining causes distortion in the final part. When modelling a multi-pass machining process, in order to predict distortion, the classical finite element method, using conforming meshes, faces limitations in flexibility and accuracy. Cutting paths cannot match the work-piece mesh before the simulation, since they are defined in the initial geometry and not in a deformed one. As a result, re-meshing is required between two machining passes. In order to circumvent these limitations, an innovative approach based on the level-set method has been developed in order to define cutting paths independently of the work-piece mesh. The proposed approach is applied to simulating milling of an airfoil.