A finite element formulation to deal with the flow of metal that includes high speed effects is presented. The deformation process of the metal is treated using the rigid-plastic or the rigid-viscoplastic approach and the solution technique used includes convective and acceleration effects in the equilibrium equations of the problem. In the first part of the paper the mechanical aspects of high speed metal forming processes are analyzed, then the solution procedures using the finite element method are developed. An interesting version of the three-field approach is presented to obtain an accurate solution for the stress field. Then the last part of the paper presents the results obtained for the steady state wire-drawing process, the steady stare extrusion problem, the steady state rolling problem and a deep drawing problem. The results obtained are compared with experimental ones and with results obtained from the quasi-static case. It is clearly shown that in some cases of industrial relevance, it is necessary to take into account of dynamic effects to obtain a good agreement with the experiments.