This paper is concerned with vibration analysis considering fluid-structure interaction (FSI) in liquid-filled pipe system using transfer matrix method (TMM) in frequency domain.The emphasis is placing specially upon the multi-span pipe system with middle rigid constraints.Three major mechanisms of coupling, the friction coupling,the Poisson coupling and the junction coupling,as well as both distributed and concentrated external excitations are considered in this study.A phenomenon associated with the rigid constraints,namely,a junction coupling depending on the Poisson coupling and friction coupling (might be called the conditional junction coupling),is revealed and discussed. Numerical examples indicate that the conditional junction coupling has much larger influence on the frequencies of a liquid-filled pipe system than the Poisson coupling does.It is also shown through the numerical examples that the proposed method is efficient.