A two-phase topology optimization method is proposed, determines not only the ratio of the phases of high and low stiffness at each point of the body, but also the angle of rotation of the axes of anisotropy. The proposed method makes it possible to significantly improve the functionality of the products being developed. The topology optimization of the two-phase material is implemented using the method of moving asymptotes, and the angle of rotation of the anisotropy axes is aligned along the main axes of the stress tensor. As an example, a rectangular elastic plate is considered, with joint constraints in the two lower corners and the force in the middle of the upper face. The problem of simultaneous optimization of phases and axes of anisotropy is solved for this plate. The obtained results are analyzed, after which the correctness of the developed algorithm is concluded.