Abstract: Based on the engineering background of liquid-filled spacecraft, the nonlinear dynamic characteristics of rigid-liquid coupling dynamic system are studied by means of multi-scale method. By using the multi-dimensional modal method, the free boundary problem describing the nonlinear sloshing of the liquid in a cylindrical tank under horizontal excitation is transformed into a finite dimensional nonlinear ordinary differential equation system in which the coupled liquid sloshing modal coefficients are assumed as state variables. The analytical expressions of sloshing force and sloshing moment acting on the tank wall caused by liquid sloshing are derived, and then the coupled dynamic equations for the spacecraft translation and liquid fuel sloshing are obtained. The dynamic characteristics, especially the first-order primary resonance, of rigid-liquid coupling system are analyzed by multi-scale method. The natural frequency of rigid-liquid coupling system is solved by the characteristic equation of natural frequency, and the amplitude-frequency response equation of liquid steady-state solution is derived when the external excitation frequency is close to the first natural frequency of coupling system. Combined with the numerical method, the amplitude-frequency response curve and excitation-amplitude response curve of liquid steady state solution are studied. The results show that with the change of liquid filling ratio, the amplitude frequency response curve of liquid steady state solution will exhibit soft, hard spring features conversion phenomenon. In addition to that, a `jump' phenomenon was also observed during this kind of soft-hard spring feature conversion. Furthermore, it is shown that the soft and hard spring characteristic conversion point of amplitude frequency response curve will be affected by gravity acceleration and spring stiffness coefficient. The above results show that the dynamic characteristics of the rigid-liquid coupling system considering the nonlinear effect are essentially different from those shown by the traditional linear system model. The investigations presented have important reference value for further analysis of rigid-liquid coupling nonlinear dynamic characteristics of liquid-filled spacecraft.