Abstract: An analytical approach to solving the galloping model for iced transmission lines based on curved-beam theory and considering elastic boundary condition was developed and can contribute to understanding the galloping mechanism. A two-degree-of-freedom galloping model is reduced from a three-degree-of-freedom galloping model according to the frequency characteristic of rotational direction, then the multi-scale method was used to deduce the 1:1 and 2:1 internal resonance simplified amplitude equations. Then, the effects of variation in the axial model function brought about by the difference between DOF reduction methods and the elastic boundary condition on bifurcation and stability, amplitudes, and galloping critical wind velocity were identified. Results indicate that the impact of variation of the axial model function on the galloping bifurcation and stability, galloping amplitudes and critical wind velocity is slight in the 1:1 internal resonance case and, for corresponding parameters, comparatively great in the 2:1 internal resonance case, especially when not considering the eccentricity of the cross-section. When considering the eccentricity of cross-section in the 1:1 internal resonance case, unstable galloping wind velocity ranges brought about by the elastic boundary condition decrease. The influences of the elastic boundary condition on the galloping amplitudes and critical wind velocity are distinctive; the corresponding displacement amplitudes of the iced transmission line and the supercritical wind velocity decrease, the critical wind velocity increases, and the galloping wind velocity range lessens under the elastic boundary condition.