Purpose <p>The aim of this study is to clarify the effect of elastic supports and curvature of cables on wave eigenvalues and propagation characteristics.</p> Methods <p>The Hamilton principle for conservative systems was applied. An analytical coupled wave model was presented to describe responses in a cable with small curvature and elastic supports. Free wave propagation parameters were first investigated. A field test was conducted using non-contact measurement methods and its results compared to the theoretical wave velocity. Additionally, the cable free response was solved by the Fourier transform in the spatial domain.</p> Results <p>The analytical wave velocities of a catenary considering droppers were close to experimental data. Curvature not only gave rise to cut-off frequencies but also produced both fast and slow moving longitudinal waves. The elastic supports affected the wave propagation in cables in the following three ways. Firstly, they generated the cut-off transverse wave frequencies and broadened the longitudinal wave stopbands. Secondly, they caused wave dispersion at low frequencies. The phase velocity will be higher than the group velocity and the two velocities will vary with frequency at low frequencies. Finally, they added weak wave attenuation to the system, contributing to the continuous attenuation of the wave crest and the oscillatory decay of the trailing edge.</p> Conclusion <p>Results confirmed the important role of curvature and elastic supports on the cable wave eigenvalues and propagation characteristics.</p>