Multi-stable metamaterial can deform under external forces， enabling flexible manipulation of elastic wave propagation. This paper proposed two multi-stable metamaterials based on the bistable flexural elastic beam structure， with different bending dimensions. These metamaterials possess two stable configurations and can switch between these states under the external forces. The dispersion relation and frequency response characteristics of the multi-stable metamaterial in the two stable configurations were investigated by the finite element method. The results reveal that by adjusting the external applied forces， the stable structure can be deformed， effectively tuning the frequency range and bandwidth of the bandgap. A wider first bandgap range can be obtained by expanding one-dimensional multi-stable metamaterial into three-dimensional multi-stable metamaterial. This shape-changing mechanism not only provides diverse control methods for elastic wave propagation but also offers new insights into the design and application of elastic waveguide switch.