Abstract: Based on ideal fluid assumption, the coupling dynamic equations of rigid tank and nonlinear sloshing of liquid are established through H-O principle with surface tension and damping considered. The modified potential function and wave height function are introduced to describe the moving boundary of fluid and rigid tank which is forced in surge. Galerkin’s method is used to discrete the dynamics equations into ordinary differential equations. Both the movement and the motivation of rigid tank are considered. The natural frequencies of the rigid-liquid coupling system are formulated with liquid depth, the length of the tank, and etc. The nonlinear dynamics of the rigid-liquid coupling system is investigated analytically. Using the multi-scale method, the amplitude-frequency response is obtained and the jumping phenomenon is observed. It is also observed that as the depth of liquid decreases, the soft and hard characteristics transform to each other. Subsequently, the effects of all factors are studied in detail. Under the condition of giving horizontal excitation, we also can analyze the stable solution of the rigid, which is the same as liquid in qualitative analysis. Finally, compared to the numerical solution, the analytic solution proves to be feasible.