The wheel shimmy is a classical non-linear problem. The most frequently used approach to study this phenomena is based on linearized low degree of freedom models, that from one side, thanks the simplicity of the equations of the motion, allows to evaluate the stability with classical stability-analysis approach, but from the other side it limits the study about the equilibrium point. In this paper a stability-analysis, based on a three degree of freedom non-linear analytical model, is presented. Starting from the system numerical response, adopting a time-domain modal analysis method, the modal parameters were identified. The proposed procedure, through a 3 degree of freedom nonlinear representation of the castor, highlights the three main castor oscillation modes whose characteristics can then be identified with a method applicable even for experimental investigations.