This study presents a parameterized model for additively manufactured dies to control the strains in extruded profiles. As preferable state variables in the profiles are material-dependent, knowledge of the influence of geometrical parameters on the resulting strain paths is needed. To elaborate on the dependency, the die geometry is systematically parameterized, enabling the automated generation of different designs. Using finite element (FE) simulations to assess these designs, the strains during forming are analyzed. The results clarify the significance of geometrical parameters for the introduction of positive strains transversal to the extruding direction. Notably, the deflection of material within the die profoundly influences the strain paths. Varying the free-form surfaces demonstrates the capacity to achieve distinct strain profiles. This study underscores the potential of tailoring die designs to beneficial strains in the profile. Hence, the findings have significant implications for industries seeking to optimize extruded profiles' structural integrity and uniformity.