Abstract: An explicit arc-length method is proposed upon the discrete element theory to analyze the whole process of structural elastic buckling behavior. The constitutive model of a new contact element—a hinged-fixed contact element is established. The discrete element method and the structural mechanics method are used to analyze the hinged-fixed contact element under the condition of known end displacement respectively, then the contact stiffness coefficient is deduced by equalizing the internal forces obtained through these two methods. The dynamic damping technology is used to simplify the solution process of the particle motion equation. The arc-length method with total displacement constraints is introduced into the discrete element method, and the solution strategy and implementation process of combination are described in detail, also, the calculation formulas for the relevant analysis parameters are developed. The accuracy and applicability of the method are verified by some examples. The method proposed can simulate the buckling behavior of the structure without assembling the stiffness matrix and involving matrix singularity. Also, it has few parameters and good stability compared with the traditional finite element arc length method, providing a new algorithmic for structural analysis.