Estimating cable tension in cable-stayed bridges or in external tendons is essential for regular inspection and assessment of those structures. Vibration measurements provide a solution, however, may not be accurate in cases parameters such as amount of sag and bending rigidity of cable are significant. In this study, the characteristic equation for vibration of the most general case of a cable, where both the sag and flexure in the cable are taken into account, is analytically derived. After that by considering proper simplifying assumptions of small flexural rigidity parameter, asymptotic forms of that equation are obtained. It renders a practically applicable procedure to estimate cable tension using measured natural frequencies. The developed procedure is verified by realistic data of a cable stayed bridge in Vietnam.