Abstract: In order to solve the TBS (torsion bar shaft) torsional stiffness and strength for the outer support anti-rolling device in railway vehicles, an analytical method of introducing the TBS deformation coordination conditions is proposed. ［Method］ Taking 1/2 TBS for the outer support anti-rolling device as an example, based on its stress state and load distribution, the structural symmetry and the characteristics of bearing anti-symmetric working loads are used to introduce structural deformation coordination conditions for solving the unknown forces and moments of a primary statically indeterminate system, obtaining the shear force and bending moment distribution of the TBS, and deriving calculation formulas for the torsional stiffness and strength of the anti-rolling torsion bar device. Using the outer support anti-rolling torsion bar device made of 52CrMoV4 spring steel as an example, a comparative analysis is conducted between the analytical solution calculation results and the finite element model calculation results of the outer support TBS. ［Result & Conclusion］ The proposed analytical solution method can conveniently determine the stress levels and stress states at different TBS cross-sectional positions, providing a theoretical basis for determining the TBS cross-sectional geometric parameters, the equivalent stress calculation method of different critical cross-sections, and the analysis of TBS fatigue failure mechanism. Compared with the finite element method, the proposed analytical method features simple calculation principle and fast calculation speed.