In this study, the convergence of anisotropic hardening models in finite element simulations is investigated for a number of possible strain path change scenarios. To this end, the convergences of a few plasticity models are visualized through the convergence mapping technique, as in Scherzinger, W., 2017, Comput. Methods Appl. Mech 317, 526-553. The three main factors that affect convergence in the return mapping algorithms, namely, plasticity model, stress update algorithm, and magnitude of trial stress, are explored. Isotropic hardening, non-linear kinematic hardening and distortional plasticity models are employed under the plane stress condition to simulate a strain path change. In particular, the convergence maps of the HAH distortional plasticity approach for cross-loading and reverse loading are computed. Moreover, the convergence maps are established for implicit and explicit stress update algorithm schemes for various trial stresses. Based on this study, possible strategies leading to convergence improvements are discussed.