Phononic crystals (PCs) have possessed outstanding features to control/manipulate the propagation of the acoustic/sound wave. In this paper, the local resonant elements, such as local resonant cavity in fluid PCs and local resonant inclusion in solid/fluid PCs, are introduced. The effect of geometry parameters, Poisson's ratio, Young's modulus on the band gap solid/fluid PCs are investigated in detail. It is found that wider multiple band gaps are obtained for the fluid PCs with local resonant cavity of “+” hole compared with square and circle holes. More importantly, the very low-frequency band gaps can be obtained by introducing the local resonant inclusion with consideration of fluid-structural interaction for solid/fluid PCs. In addition, we have compared the sound transmission loss in fluid and solid/fluid PCs. The numerical results have clearly indicated that solid/fluids PCs with consideration of fluid-structural interaction can block the propagation of stress wave effectively compared with fluid PCs. The theoretical study and numerical simulation conducted in this work have provided a new avenue to design more innovative fluid and solid/fluid PCs.