Abstract: This paper is concemed with the dynamic coupling behavior of partially liquid-filled rectangular container under pitch excitation in the case of constant gravity. A new method is presented to establish the dynamic equations of the coupling system. Based on two different Lagrange functions, the reduced-order nonlinear coupled dynamic equations of the coupling system are obtained, resulting in significant simplification of the formulation of the problem. A numerical example is provided in which the characteristic of the coupling system is discussed. The present method can be extended to the analysis of the dynamic behavior of liquid-structure coupling of cylindrical container in the case of three-dimensional liquid sloshing.