Abstract: The coupling dynamics of the pitching of spacecraft, the sloshing of liquid fuel and the vibration of elastic appendages are investigated. The coupling dynamics equations deduced by using H-O principle are adopted. The multiple scale method is proposed to analyze the primary resonance of the rigid-liquid-elastic coupling system. The bifurcation analysis is given by means of singularity theory. The hysteresis bifurcation is found in the desired coupling system, it is represented by the amplitude-frequency response switches between soft and hard spring types at the critical depth.