With the development of science and technology and transportation, high pier and large-span bridges are rapidly rising. Due to the increase in span diameter and pier height, nonlinear and stability problems of bridges become more and more important. In this paper, the stability of large-span steel box-girder suspension bridges is investigated using engineering mechanics methods. Based on the finite element analysis method to solve the bridge structure of the first type of stability problems and the second type of stability problems, the use of the response spectrum method for bridge seismic response. Taking “Xiling Yangtze River Bridge” as the engineering background, the seismic response is analyzed by establishing a finite element model. The axial force of the bridge tower generated by the downstream earthquake is larger than that generated by the transverse earthquake. In the transverse direction, the bending moment MZ is larger than the bending moment MY in the transverse direction, and the bending moment of the pile foundation is larger than the bending moment of the pile foundation in the longitudinal direction. The Xiling Yangtze River Bridge plays a dominant role in transverse seismicity, and its downstream seismic excitation plays a dominant role in longitudinal seismicity. However, the energy-demand ratio corresponding to the transverse moment MY is only 1.83, and the strength of the pile section needs to be further improved. For the future innovation of bridge design, a high-performance bridge structure based on UHPC is an important direction for future development.