Dome structures have been built as roofs for venues where many people convene. Failure of this type of structure may jeopardize the safety of hundreds or even thousands people. For this type of structure, snap-through buckling may occur in a local area and gradually expand to the entire structure, leading to a failure of the overall structure. Although numerous structural health monitoring techniques and damage detection approaches have been developed, no research on the detection of a snap-through buckling has been reported. The objective of this study is to find a signature that is sensitive to snap-Through buckling in dome structures and can be used to detect snap-Through buckling. Considering that a snap-Through buckling results in a significant deformation in a local area, which can be reflected by the change in tilting angles of members in that local area, the change in tilting angles of members will be proposed to be a signature to detect snap-through buckling. To verify the proposed instability signature, a reticulated dome structure will be investigated. Both an eigenvalue buckling analysis and a nonlinear buckling analysis will be conducted. The significant changes in tilting angles of members in the buckled regions have demonstrated the efficacy of the proposed instability signature. This research will bridge the research gap between structural health monitoring and structural stability research.