Wind-excited vibrations generated by vortex shedding are very common in high-voltage overhead transmission lines. Although such vibrations are barely perceptible due to their low amplitudes (less than a conductor diameter), they are, however, extremely important since they may lead to conductor fatigue. Mathematical models are therefore necessary for the computation of these vibrations, in order to evaluate the risk of potential damage to the line as well as for studying the efficiency of damping measures. For single conductor lines, the socalled energy-balance method gives good results in estimating the vibration amplitudes. However, the problem becomes more involved for bundled conductors with spacer dampers, commonly used in high-power transmission in many countries, and a modified form of the energy-balance method is presented here. Singular perturbation methods are employed, along with the energetically equivalent standing wave amplitudes obtained from the modified energy-balance methods, to determine the bending strains at critical points. This gives an estimate for the maximum strain levels in a conductor, which can be very useful in the design of transmission lines and for the optimization of the corresponding damping devices.