A plasto-hydrodynamic lubrication model dedicated to metal forming processes is presented in this paper. A finite element formulation for the fluid-solid interaction problem is given, as well as an effective calculation procedure for solving the resulting non-linear equation system. A computer simulation of the processes of lubricant film formation and transportation in the upsetting of a metal cylindrical billet illustrates the validity of the proposed model. The thickness of the entrapped film at the instant of depression closure and its variation as compression proceeds are discussed and compared with the results given by previous researchers.