Aeolian vibrations in the frequency range of 10-50 Hz are ubiquitous in the conductors of transmission lines. They are usually not perceptible to the casual observers due to their small amplitudes, nevertheless, they are important as they may lead to failure of the lines through material fatigue. These problems become more severe for long-span lines. Since the conductors are fabricated in finite lengths, every once in a while two conductors have to be connected in the field, using appropriate fittings. A particular case of fitting, considered in this paper, is the compression splice bushing (CSB), which is sometimes used in long spans to join the ends of two conductors. It is desired to estimate the values of the maximum bending stress developed in the conductors and in related fittings due to aeolian vibrations. An obvious approach would be to solve the boundary value problem for the conductors with the CSB; here a model is presented that avoids the solutions of the complete boundary value problem and results in solving a set of linear algebraic equations. © 2006 Elsevier Ltd. All rights reserved.