This paper focuses on the application of different tyre models to analyse the shimmy phenomenon. Tyre models with the Magic Formula and a non-constant relaxation length are introduced. The energy flow method is applied to compare these tyre models. A trailing wheel suspension is used to analyse shimmy stability and to evaluate the differences between tyre models. Linearisation and nonlinear techniques, including bifurcation analysis, are applied to analyse this system. Extending the suspension model with lateral flexibility and structural damping reveals more information on shimmy stability. Although the nonlinear tyre models do not change the stability of equilibria, they determine the magnitude of the oscillation. It is concluded that the non-constant relaxation length should be included in the shimmy analysis for more accurate results at large amplitude.