Acoustic-induced vibration in piping system and other devices leads to premature wear and failure. Especially, in nuclear power plants, very high velocity and temperature gas flows inside pipe systems. Moreover, if a frequency due to the vibration in the piping system is overlapped with a natural frequency of the stud pipe, the magnitude of the amplitude will be increased resulting in severe failure. For example, damage can be considered as flow-induced acoustic resonance at the branch pipes of the safety relief valve in the main steam lines. Specially, the pipe system not only has multi-branches but also includes the elbow that the resonance could occurs making pressure oscillation stronger than that of a single branch because of the interaction between the branches and the elbow. This study has investigated a Computational Fluid Dynamics (CFD) analysis methodology to predict and quantify the vortex shedding frequencies and the pressure pulsation magnitude in the dead-end pipe. The influence of the pressure fluctuation amplitude between each branch, number of branch, and elbow is also investigated.