One of the important parameters in the design of transmission lines is the evaluation of the susceptibility of these cables to vibrations and if necessary, providing proper means to mitigate these vibrations. Transmission lines are especially susceptible to vibrations as a result of their light weight. Viscous dampers are one of the tools that can be applied to mitigate cable vibrations. However, the damping ratio obtained by these dampers is very limited. The present study provides a finite element formulation for an isoparametric cable element. A comparison is made between the results of presented approach with finite series method to validate the model. Additionally, a comparison is made between linear and non-linear behavior of a cable under sweep sinusoidal excitations with different amplitudes. Finally, a case study is conducted to investigate the potential of additional damping provided by a third viscous damper for the case in which two rubber bushings are already attached to the cable near the anchorages. Based on this case study, the dependency between the third damper location and optimum viscosity for maximum vibration mitigation that can be given to a cable with rubber bushings is investigated. The results of the present study show that although rubber bushings may help mitigating vibrations, they reduce the effect of additional damping devices. Additionally, for non-sagged cables, the nonlinearity is negligible in moderate vibrations. Lastly, if the third damper viscosity is selected properly, it can be very effective in further mitigating the vibrations amplitudes.