The problem of flexible structure vibration isolation on a flexible foundation is analytically investigated by simplifying the vibration isolation as single axis isolation, which can be realized by a proper design, and the problem of the whole spacecraft vibration is taken as an example for the application as both the spacecraft (isolated structure) and the launch vehicle (foundation) are flexible structures. A numerical example of the whole spacecraft vibration isolation is also provided for further explaining those conclusions derived from the analytical studies. It is found from the study that the isolator’s damping is important for attenuating the vibration and that weakening the isolator’s stiffness has the same effect as increasing its damping. However, a weaker stiffness means a weaker coupling among the structures and may magnify the vibration at some resonant frequencies, which are close to those of individual structures. The coupling effect of the structure’s flexibility on the isolation may be significant in some cases and a coupling analysis is essential for ensuring the isolation performance. Because of the importance of the isolator’s damping in reducing the vibration transmissibility and the vibration of the coupled structure, it is more appropriate to describe the vibration isolation of the flexible structure as vibration attenuation.