Abstract: A continuum dynamic model is a significant tool for the continuous parametric analysis and health monitoring benchmark verification of suspension bridges. The spatial coupling of the main cable and hanger, and the internal self-balance and elastic coordination among subsystems are the core factors restricting the modeling and solution of the high-precision free vibration continuum model of self-anchored suspension bridge with spatial cables. The deflection theory is extended to the vibration form, the spatial coupling deformation equation of the main cable-hanger-girder considering the effect of hanger extensibility, and the compatibility equation considering self-balance is derived. The free vibration continuum model considering the effect of hanger extensibility is established and dimensionless, to identify the characteristic parameters controlling the dynamic characteristics. The continuum model is transformed into matrix form by the Galerkin method to solve its modal frequencies and mode shapes. The accuracy and universality of the continuum model are verified by using the calculation examples of a self-anchored suspension bridge with parallel cables in the reference and the finite element model of a self-anchored suspension bridge with spatial cables, and the sensitivity of crux characteristic parameters is analyzed. The analysis results show that, the relative elastic axial stiffness of the hanger is sensitive to the relative elastic bending stiffness of the main girder. Whether to consider the effect of hanger extensibility will affect the high-order modal frequencies, especially the antisymmetric modes. The horizontal angle of the inclined hanger plane has little effect on the modal frequencies, while the higher-order frequencies are not affected by it. The relative elastic bending stiffness of the main girder significantly affects the modal frequencies and leads to the phenomenon of modal cross-over, the elastic stiffness of the main cable only slightly affects the low-order symmetric modal frequencies. In conclusion, the continuum model considering the effect of hanger extensibility is more accurate, which can carry out continuous parametric analysis of dynamic characteristics and serve as a benchmark analytical model to provide necessary predata for preliminary design, model updating and damage identification.