Distortional hardening describes that the yield surface is deformed and has high curvature in one direction and spans a region of lower curvature in the other directions and it is observed from the experiments of many metal and alloys. To model a yield surface with such a shape, a quadratic yield function is insufficient, and a cubic polynomial of stress is the simplest available option and an elastoplastic model featuring an evolving cubic distortional yield surface has been proposed. Since the internal symmetry of this model, the projective orthochronous Poincaré group PSE_0(6,1), has also been explored, the closed-form formula of stress response under rectilinear strain-controlled paths is obtained. Based on the model and its internal symmetry, this study developed a numerical integration for the model under cyclic strain-controlled loading. Therefore, the stress response under cyclic loading was determined and the evolution of internal variables of the model was displayed. Furthermore, the evolution of yield surface in the axial-torsional-hoop stress space was observed during the cyclic loading.