How to apply Lagrange equation to elastodynamics has always been a theoretical research topic at home and abroad. After solving such problems,the theoretical difficulties of Lagrange equation applied to the coupling dynamics are placed before us. In this paper,the Lagrange equation was successfully applied to the nonconservative nonlinear rigidthermoselastic coupling dynamics by using the LagrangeHamilton system. Then the governing equations of nonconservative nonlinear rigidthermoselastic coupling dynamics were derived by using the Lagrange equation of nonconservative nonlinear rigidthermoselastic coupling dynamics. Finally, the way to solve practical engineering problems by using Lagrange equation of coupled dynamics was discussed.