Abstract: As a basic structural member, elastic beam structures are widely used in architecture, aviation, aerospace, shipbuilding, and other engineering fields. To suppress the vibration level of elastic beam structures effectively, it is of great significance to understand their vibration characteristics and dynamic responses. This manuscript establishes the vibration analysis model of the axially loaded beam structure with the nonlinear support and elastic boundary constraints. Dynamic behavior of the beam structure is predicted by applying the Galerkin truncated method. Mode functions of the axially loaded beam structure with elastic boundary constraints are selected as the trial and weight function in Galerkin truncated method. Firstly, the influence of the truncated number on the stability of the Galerkin truncated method is studied and the reliability of the Galerkin truncated method is verified by the harmonic balance method. On this basis, the influence of the sweep direction of the harmonic excitation and the parameters of the nonlinear support on the dynamic responses of the axially loaded beam structure with nonlinear supports and elastic boundary constraints is studied. The results show that dynamic responses of the axially loaded beam with the nonlinear support and elastic boundary constraints are sensitive to the initial values of calculation. Parameters of the nonlinear support significantly affect the dynamic responses of the axially loaded beam with the nonlinear support and elastic boundary constraints. In certain parameters of the nonlinear support, the complex dynamic behavior of the beam structure with the nonlinear support and elastic boundary constraints appears. Appropriate parameters of the nonlinear support can suppress the complex dynamic behavior of the axially loaded beam structure with the nonlinear support and elastic boundary constraints. Meanwhile, appropriate parameters of the nonlinear support can also suppress the vibration level at both ends of the axially loaded beam structure with the nonlinear support and elastic boundary constraints.