A finite element model is developed to predict the vibrational response of a single conductor with a Stockbride damper. The mathematical model accounts for the two-way coupling between the conductor and the damper. A two-part numerical analysis using MATLAB is presented to simulate the response of the system. The first part deals with the vibration of the conductor without a damper. The results indicate that longer span conductors without dampers are susceptible to fatigue failure.In the second part, a damper is attached to the conductor and the effects of the excitation frequency, the damper mass, and the damper location are investigated. This investigation shows that the presence of a properly positioned damper on the conductor significantly reduces fatigue failure.