A set of nonlinear partial differential equations was used to describe the motions of an internal flowing system, with the consideration of transient fluid structure interaction (FSI). The stabitity characteristics of the system were analyzed on the basis of the nonlinear FSI equation model. The results show that the stability of the nonlinear FSI system become very complicated because of the influence of strongly couplied interaction between flowing liquid and vibrating pipe. The flowing velocity, pressure, the piping stiffness, and constrained conditions, etc. play a very important role in developing procedure of the system stabilization. In an analysis example given in this paper, for example, when the flowing pressure is comparatively small, the system exhibits flutter instability, and when the flowng pressure is increases to a specified value, a subcritical divergence and a supercritical flutter bifurcation take successively place in the same velocity range. A set of nonlinear partial differential equations was used to describe the motions of an internal flowing system, with the consideration of transient fluid structure interaction (FSI). The stabitity characteristics of the system were analyzed on the basis of the nonlinear FSI equation model. The results show that the stability of the nonlinear FSI system become very complicated because of the influence of strongly governing interaction between flowing liquid and vibrating pipe. The flowing velocity, pressure, the piping stiffness, and constrained conditions, etc. play a very important role in in an analysis example given in this paper, for example, when the flowing pressure is comparatively small, the system exhibits flutter instability, and when the flowng pressure is increased to a specified value, a subcritical divergence and a supercritical flutter bifurcation take connected place in the same velocity range.