Equations of motion are derived for a flexible orbiting spacecraft, consisting of a rigid base body, a flexible beam and a rigid tip body, taking the motion of instantaneous centre of mass into consideration. We consider three kinds of motions, namely, the attitude motion of the base body, the three-dimensional translational vibrations (extension in the longitudinal direction and bendings in the other two directions) and the torsional vibration of the flexible beam due to the existence of the rigid tip body. It is shown that the motion of the base body and the motion of the flexible beam are coupled to each other. The translational vibrations and the torsional vibration of the flexible beam are also coupled through the dynamics of the tip body. One interesting aspect is that, as an effect of the interaction between the rigid base and the beam, a perturbation term appears in the dynamic equation of the flexible beam. It is also made clear that, fortunately, the existence of this perturbation leads only to an increase in the stiffness of thg flexible beam and does not affect damping of the vibration. Finally, the control design problem is mentioned and computer simulations are discussed.