Phononic crystals (PCs) have attracted plenty of attention during the past two decades, and a lot of work has been devoted to the numerical, theoretical and experimental analysis of the band gaps of the PCs with 1D, 2D and 3D structures, respectively. The band gaps have been found to be related to the topology of the unit cell, filling ratio, contrast of the material properties between matrix and inclusion, and so on. However, they are fixed when the fabrication of corresponding devices is finished in most cases. Usually, biasing fields (e.g. initial stress, initial deformation, pre-existing electric field, external electric field and magnetic field, etc.) can be utilized to tailor the band gaps in flexible and reconfigurable ways. Recently, the instability-induced deformations triggered by external mechanical loadings have been found to be an effective and reversible way to tune the band gaps and the directionality of PCs made from soft materials, such as silicon and rubber. In this project, a novel design of PCs will be proposed, which consists of perforated plate with some individual beams fixed on the boundary of internal holes. When the external mechanical loading applied on the PCs reaches a threshold value, instability-induced buckling will be triggered and the internal beams might be in contact with each other, which will significantly alter the topology of PCs, and therefore effectively tune the band gaps of PCs. A systematical analysis will be carried out to study the influences on the tunability of PCs with different designs through finite element methods (FEM).