The effects of the anisotropy evolution and of the directionality in hardening on the predictions of the earing profile of a strongly textured aluminum alloy are investigated using a new distortional hardening model that incorporates multiple hardening curves corresponding to uniaxial tension along several orientations with respect to the rolling direction, and to biaxial tension. Yielding is described using a form of CPB06ex2 yield function (Plunkett et al. (2008)) which is tailored for metals with no tension‐compression asymmetry. It is shown that even if directional hardening and its evolution are neglected, this yield function predicts a cup with eight ears as was observed experimentally. However, directional hardening can be of considerable importance for improved accuracy in prediction of the non‐uniformity of the cup height profile.