An anisotropic (texture based) fourth order strain-rate potential is directly used in an elastoplastic finite element code (ABAQUS). The method is based on the Taylor model of crystal plasticity and therefore takes the initial texture, texture evolution and its influence on deformation-induced anisotropy into consideration. The deep drawing simulations of cold-rolled and annealed aluminum sheets with different texture intensities are carried out using this code in conjunction with the UMAT subroutine. The full geometry of deep drawing tools and friction effect are also taken into account in these simulations by employing shell elements. Comparison of the predicted and measured ear profiles is conducted. Reasonable agreement is obtained between the predicted and measured earing profiles for strong and weak textured sheets. The trend of the influence of texture evolution on earing behavior is clearly demonstrated. The predictions for annealed aluminum sheets are much better than the rolled ones. The earing characteristic of ideal textures appearing in aluminum sheets is also discussed. It is shown that Cu component exhibits lower earing cup in deformation texture components appearing in aluminum sheets.