The mechanical properties of the panel structure must be improved because the steel frame panel contributes to the stress of the whole building structure and bears some part of the external load of the steel frame members. The rib-stiffened panel can achieve a good connection with the outer frame and improve the mechanical performance of the whole structure. Therefore, the mechanical instability performance of the steel frame rib-stiffened panel structures is investigated in this study. Here, the dynamic analysis method is used to calculate the displacement of the panel structure. The stability of the panel structure can be judged according to the displacement value; thus, the stability of the panel structure can be ensured. The example test results denote that the hysteretic curve shape exhibits the characteristics of the shuttle hysteretic curve, and the whole structure exhibits plastic deformation performance and aseismic performance after being subjected to tension; the skeleton curve denotes that the bearing capacity of the test specimens can satisfy the requirement of elastic design with respect to the wall panel structure in the first stage and achieve the elastic-plastic seismic design and ductility requirements in the second stage. The proposed detection model can judge the instability of the steel panel structures.