AbstractThis paper focuses on the simulation of earings in deep drawing of cups by means of a recently developed anisotropic constitutive model. The model is derived in a thermodynamicallyconsistent framework and includes nonlinear kinematic and isotropic hardening. It represents a multiplicative formulation of anisotropic finite elastoplasticity in the finite strain regime. The description of anisotropy is characterized by the use of the so‐called structure tensors as additional tensor‐valued arguments in the representation of the yield function and the plastic flow rule. The evolution equations are integrated by a form of the exponential map that retains the plastic volume and uses the spectral decomposition to evaluate the exponential tensor functions in closed form. Finally, finite element simulations of cylindrical cup drawing processes are performed and the predicted earings are compared to results from experiments (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)