The stability of liquid filled spacecraft with flexible appendage was researched by using energy-Casimir method. Liquid sloshing dynamics was simplified by spring-mass model, and flexible appendage was modeled as a linear shearing beam. Rigid-liquid-flexible coupling dynamics of spacecraft was built. The energy function and the Casimir function were derived by analyzing the energy function of a rigid body, liquid sloshing and a flexible appendage. The nonlinear stability condition of coupled spacecraft system was derived by computing the first and second variation of energy-Casimir function. The stable and unstable regions of the parameter space were given in the final section with numerical computation. Related results show that the inertia matrix, the length of shearing beam, the spacecraft spinning rate, and the filled ratio of liquid fuel tank have strong influence on the stability of coupled spacecraft system.