Most of the constitutive models for metallic materials assume yield functions of von Mises or generalized Tsai-Wu type. Isotropic and/or kinematic evolutions are developed for hardening, which correspond to affin expansions or simple shifting of original yield surfaces, whereas experimental results show a distinctive change of the shape of yield surfaces (rotated or dented) depending on loading conditions and load paths. To cover the material behaviour with distorted yield surfaces a hierarchical expansion of yield functions to hardening tensors of the fourth and the sixth order is proposed. Parameters of corresponding evolutionary equations are determined by model parameter optimization. The extended model is investigated comparing numerical results to cyclic experimental data in biaxial σ-τ space.