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Low-nickel austenitic steel is subjected to high-pressure torsion fatigue (HPTF) loading, where a constant axial compression is overlaid with a cyclic torsion. The focus of this work lies on investigating whether isotropic J2 plasticity or crystal plasticity can describe the mechanical behavior during HPTF loading, particularly focusing on the axial creep deformation seen in the experiment. The results indicate that a J2 plasticity model with an associated flow rule fails to describe the axial creep behavior. In contrast, a micromechanical model based on an empirical crystal plasticity law with kinematic hardening described by the Ohno–Wang rule can match the HPTF experiments quite accurately. Hence, our results confirm the versatility of crystal plasticity in combination with microstructural models to describe the mechanical behavior of materials under reversing multiaxial loading situations.