Abstract <p>Towed wheel shimmy is a common nonlinear vibration in the landing gear of aircrafts, which can pose serious safety hazards to aircrafts. In order to analyze and predict the vibration amplitude of the towed wheel shimmy, a two degrees-of-freedom (DOF) mathematical model is established. Then, the Newton interpolation method is used to modify the incremental harmonic balance (IHB) method. On this basis, the amplitude of the towed wheel shimmy is semi-analytically solved and predicted for different speeds and lateral damping of the suspension, the results are verified with the help of numerical integrations. In addition, the three-dimensional diagram of the system response for different speeds and lateral damping is obtained by using the modified IHB method, the influence of the lateral damping of the towed wheel is studied. The results indicate the modified IHB method can accurately predict the vibration amplitude of the towed wheel shimmy for different parameters, and the increase of the lateral damping of the suspension is effective for suppressing shimmy.</p>