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The tower crane is a typical soaring and complex frame structure, and buckling is an important factor affecting its safety and carrying capacity. Considering the special characteristics of the boundary conditions for the boom structure, a numerical analysis method based on movable boundaries is proposed in this paper. In order to demonstrate the accuracy of the method, numerical analysis and stress tests are carried out on the tower crane. The results show that the numerical results are basically consistent with the experimental results. A geometric buckling analysis for extremely severe conditions is carried out in order to understand the buckling behaviors. The failure modes and complete load-response curves obtained for the tower crane are comprehensively analyzed. A dual (geometric and material) nonlinear buckling analysis of the tower crane is then investigated. Finally, the influences of the deflection load parameters on the buckling response of the tower crane are explored. It is demonstrated that bifurcation point buckling and limiting point buckling are excited by different deflection load parameters, respectively. The proposed method can accurately predict the buckling of the tower cranes, given the coupling of structure and mechanism, to ensure the safety of giant cranes in actual engineering use.