A complete analysis was made for an isotropic hardening rate-type elastoplastic constitutive model with the logarithmic stress rate utilizing solid shafts torsion test in the large strain range. The deformation rate, the logarithmic spin, the Kirchhoff stress and the logarithmic stress rate of the Kirchhoff stress were obtained for the free-end solid shaft torsion test when considering Swift effect. Utilizing the results obtained from the solid shaft torsion test, the plastic rigidity function in the isotropic hardening elastoplastic constitutive model was determined at finite strain range. It was shown that the influence of Swift effect on finite strain constitutive model was related to the varying rate of axial deformation and the varying rate of radius deformation to shear strain, and the plastic rigidity function corresponding to the logarithmic stress rate was the same as that corresponding to the Jaumann stress rate when neglecting Swift effect. Solid shaft can achieve very large strain without buckling in torsion test. They can be used to accurately determine the large strain elastoplastic behavior [1-3]. Many researchers are interesting in the theoretical study and experimental study on large strain torsion deformation [1-7]. Jaumann objective stress rate is often adopted for study on constitutive models , but Nagtegaa J C  discovered that Jaumann stress rate may render oscillatory stress response for anisotropic kinematics hardening simple shear problem. After that, great interests focus on the issues of choosing an appropriate objective stress rate in rate type constitutive models. The expression of logarithmic stress rate with logarithmic spin can be found in Xiao H . It had been proved that among all rate type elastoplastic constitutive models, only those with the newly discovered logarithmic stress rate fulfill the self-consistency criterion. In this paper, the parameter in large strain isotropic hardening elastoplastic constitutive model is determined with logarithmic rate of Kirchhoff stress utilizing solid shaft torsion test.