In the contribution at hand, the quadratic Hill yield function is extended to a finite strain, multiplicative kinematic framework. Furthermore, it is expanded by a novel combination of linear and exponential hardening. The formulation is derived in a consistent manner. Subsequently, the capabilities to model Ti-6Al-4V in a realistic manner are demonstrated, considering the anisotropy in plastic material behavior, which is induced by additive manufacturing. Therefore, different tensile tests from the literature are simulated, and a validation is carried out. Finally, the significance of the anisotropy is demonstrated in a numerical example. The maximal force obtained in the simulation is shown to be significantly different, if the building direction is considered.