Abstract: Based on the generalized potential energy variational principle of nonlinear elasticity theory with large deflection, an incomplete generalized potential energy functional for free vibrations of three-span self–anchored suspension bridges is established by considering the coupling of flexural and axial deformation, shear strain energy and torsion strain energy of stiffening girder. Neglecting nonlinear terms, the linear vertical vibrational differential equations are obtained through constraint variation. A concrete self-anchored suspension bridge with main span of 240 meters is taken as an example. The analytical results of frequency coincide with those of numerical methods. It is believed that the present method can provide a theoretical basis for the analysis of free vibrations of self-anchored suspension bridges.