A major part of central European infrastructure buildings was designed decades ago and has different needs of strengthening. Increasing traffic volume, increasing axle loads, and a growth in transport volume as well as more restrictive design rules are the reasons why the support regions of existing bridges and flat slabs often show a lack of punching resistance today. At the University of Innsbruck, a system for subsequent strengthening by the use of concrete screws was developed. Various laboratory tests showed that the system leads to a significant increase of punching resistance with minimal efforts for its installation. This article deals with the development of a numerical model that can predict the punching loads of unstrengthened and screwstrengthened punching plates. Further the punching loads from the laboratory tests and the simulations are compared to the predictions of a design approach. The presented novel design approach is an advancement of the existing Eurocode 2 provisions and allows the influence of the screws on the punching resistance to be taken into account. The comparison shows that the numerical model predicts the punching resistances in an appropriate way and the design approach predicts them on the safe side. The presented design approach was included into the technical assessment for the concrete screws of the system reLAST as post-installed punching reinforcement system [Z-15.1-340 (2019)] in order to be applicable in practice.