Abstract: Stability of stationary motion for a rigid Body with a flexible beam wasinvestigated, and both of translation and attitude motion were underconsideration. Quasi-coordinates play an important role in electing statevariables. The Lyapunov functional was constructed by the first integrals ofthe dynamical equations. The state variables introduced in this papersimplify the Lyapunov functional, and make stability analyse easy. As aresult, the sufficient conditions for the normal stability of two classes ofstationary motion were given.