An arbitrary Lagrangian-Eulerian model is described for the prediction of metal flow in a steady-state forming process. The formulation is shown to be capable of dealing with free surface and boundary friction; the coupling with thermal effects is also considered. The numerical techniques are based on the finite elements for spatial discretization of the momentum equation and on an explicit integration scheme for discretization relative to time. The mass and energy equations are integrated by a finite-volume method. Details on the application to an orthogonal cutting process are given in the final Section of the paper.