The tire deformation traveling wave varies at different vibration frequencies and speeds, and is influenced by the coupling of landing gear structural vibration, resulting in continuous changes in tire lateral deformation modes. The tire models for previous traditional landing gear shimmy analysis are quasi-static restoring force model , which assume that the functional relationship between tire lateral force, self-aligning moment and lateral deformation was fixed. Based on the tire stretched string theory, a time delay tire model coupled with landing gear shimmy is established to analyze the dynamic changes in tire lateral deformation modes, the real-time lateral deformation distribution of the tire and the nonlinear dynamic behavior of the landing gear during shimmy are obtained. The time delay is introduced to calculate the tire deformation traveling wave, the stability of the landing gear tire coupled shimmy model is studied by the bisection method. The testing methods for the parameters of time delay tire shimmy model is provided. Using the methods presented in this paper, the landing gear shimmy analysis and experimental test of a certain aircraft are conducted. The calculated vibration frequency and shimmy stability region are consistent with the analysis results of traditional tire models and test results.