An analytical model of a single line transmission line carrying a Stockbridge damper is developed based on the Euler–Bernoulli beam theory. The conductor is modeled as an axially loaded beam and the messenger is represented as a beam with a tip mass at each end. Experiments are conducted to validate the proposed model. An explicit expression is presented for the damping ratio of the conductor. Numerical examples show that the proposed model is more accurate than the models found in the literature. Parametric studies indicate that the response of the conductor significantly depends on the excitation frequency, the location of the damper, and the damper parameters.