Accurate predictions concerning a forging process can be obtained by numerical simulation, but only with a thorough knowledge of the main process variables. The material flow behavior and the interface effects are already well studied in the literature, but not the machine behavior, although it is required to estimate blow efficiency and deduce the energy actually transmitted to the workpiece. In this paper, an experimental methodology was applied to determine a spring-mass-damping model and its associated parameters for a screw press. The model and its parameters were identified with press strikes performed without billet. For validation, simulations were performed to predict blows on copper billets. The model’s predictions were in good agreement with the experimental measurements for ten consecutive blows on a copper billet. The decrease of process efficiency and the evolution from inelastic blows to elastic blows were correctly depicted by the model.