The knowledge of interaction between press, forming tool and process is essential for the quality of formed parts. Since implementing press characteristics is challenging, this paper introduces a generic formulation of an interactive digital twin representing the elastic machine behavior. Parametrized with one set of measurement data, the generic twin enables the interactive determination of the press's elastic deflection for any forming tool, saving FEA during tool development. Decreasing the influence of the individual measurement increases the applicability of the acquired information and its application range. As a result of the early and direct application of the elastic machine behavior during tool development, the manufacturing cost is reduced, and agility is increased due to enhanced flexibility and shorter iteration cycles.