This paper presents a study of the lateral vibrations of straight and curved cables with no axial pre-load. For the computation of the vibration transmissibility we used finite elements based on the Euler–Bernoulli theory. The dissipation of energy was studied with viscous- and structural-damping models, where the Rayleigh coefficients and the frequency dependence of the loss factor were identified. By using the equality between the measured and the computed natural frequencies the frequency dependence of the dynamic modulus of elasticity was estimated and used for all the studied types of cable. The excitation was the result of moving the support in a direction perpendicular to the axis of the cable. The mathematical model for the computation of the vibrations of the straight and curved cables was verified with experimental measurements in which the support excitation was achieved with an electrodynamic shaker and the amplitude force was measured at the fixed support with a dynamometer. For the curved cable the mathematical model was verified for in-plane and out-off-plane vibrations. Three straight cables of different lengths were analyzed for the dependence of the Rayleigh coefficients on the length of the cables.