With the increasing span of cable-stayed bridges, the towers are getting higher and higher, and the stiffening beams are becoming more and more slender. The increase in span causes the axial pressure of the beams and towers to increase rapidly, and the sag effect of the cables, geometric nonlinearity, and material nonlinear effects are significantly increased. The influence of these disadvantages greatly reduces the stability of the cable-stayed bridge, and the stability of the cable-stayed bridge becomes prominent. In this paper, the finite element method is used to analyze the first kind of stability problem and the second kind of stability problem of cable-stayed bridges. On this basis, a large-span prestressed concrete (PC) cable-stayed bridge is taken as an example to analyze and compare the two types of stability problems of the bridge during the construction phase and the operation phase. Besides, the model experimental study on the stability of the bridge during the maximum double cantilever construction period was carried out. The theoretical values and the model test results are compared to verify the correctness of the calculation method and design theory, which may provide a reference for the design, construction, and scientific research of cable-stayed bridges.