Rapid tooling has become an effective solution for reducing time and costs in tool production. In sheet metal forming, polymer tools produced via additive manufacturing offer performance comparable to traditional tools. However, a key challenge in this area is compensating for the radial expansion of polymer tools during the forming process, which leads to reduced accuracy in the produced parts and limits the achievable forming depth. To address this issue, the authors of this study proposed a novel punch design aimed at containing radial expansion, thereby enabling greater drawing depth and improved part accuracy. Different punch geometries were designed with a re-entrant angle varying between 150° and 180°. Numerical simulations were conducted to evaluate the optimal geometry, identifying the 160° angle as the best option to compensate for radial expansion and reduce punch load. Experimental tests were then performed to verify the numerical results, demonstrating the potential of this new design producing cups with higher drawing depth and best radial accuracy.