Abstract The paper reports an investigation on a continuous model for dynamics of large-diameter sagged cables, taking bending stiffness and sag extensibility into account. Following the classical guidelines of cable dynamics, and by making some simplifications, a continuous model is found in this work; frequency and mode shape equations have been obtained in non-dimensional form. Comparison with Finite Element (FE) and Finite Difference (FD) models has been made to validate the proposed method. Moreover, it allows us to represent local effects at the end zones of cable correctly, if clamped boundary conditions are assumed. To obtain comparable results, the FE model would require a large subdivision, with consequently, a large number of elements. The proposed eigenfunctions allow us to solve the dynamic problem without a large computational effort compared to FE or FD approaches. Finally, in order to show the usefulness of the developed continuous model, an application on the main cables of the designed Messina Strait Bridge has been made.