A novel model is developed for a vibrating single-conductor transmission line carrying Stockbridge dampers. Experiments are performed to determine the equivalent viscous damping of the damper. This damper is then reduced to an equivalent discrete mass-spring-mass and viscous damping system. The equations of motion of the model are derived using Hamilton’s principle and explicit expressions are determined for the frequency equation, and mode shapes. The proposed model is verified using experimental and finite element results from the literature. This proposed model excellently captures free vibration characteristics of the system and the vibration level of the conductor, but performs poorly in regard to the vibration of the counterweights.