Cables are used in different engineering fields, due to their usefulness in carrying payloads, transmitting power and signals over long distances. Structural cables form an integral part of civil engineering structures like long span bridges, tall buildings, marine cables and transmission towers. These flexible cables offer significant axial tensile load carrying capacity. On the other hand, cables are prone to vibration, due to their high flexibility, relatively small mass and very low inherent damping characteristics. As a result, cable structures are more susceptible to vibration under wind loads and seismic excitations. One of the major cable structures subjected to these excitations is cable-stayed bridge. Low inherent damping of cables needs to be supported by control measures to mitigate such excessive vibration levels. The objective of this study is to understand the dynamic behaviour of stay cable under support excitations and develop a semi-active control algorithm using Magnetorheological (MR) damper as an actuator to suppress the vibration amplitude. To start with, the vibration behaviour of cables is considered. A case of horizontal cable is taken for initial study, which is initially assumed to be inextensible. The static displacement of a cable due to gravity, or cable sag is taken into account. Sag results in cables having complex dynamic behaviour. This is seen when the nonlinear equations of motion for an inclined cable are developed. To model the inclined cable vibrations, Galerkin’s method is used to convert the nonlinear partial differential equations into a set of modal equations. The governing equations of motion are then solved numerically to study the cable behaviour for free vibrations and under support excitations. For vibration mitigation, a semi-active control technique is proposed using MR damper as an actuator. Different models have been studied for modelling of MR damper characteristics. The modified Bouc-Wen model is chosen from literature to model the MR damper and numerical simulations are carried out to establish the behaviour of the damper in relation with its characteristic parameters and to understand the dependence on applied voltage (or current). Finally, a semi-active control algorithm is developed for cable vibration problem. A bilinear state space form forms the basis for controller development. The control is achieved in two stages: a primary controller that assures global asymptotic stability of cable system is designed based on Lyapunov direct method, and in secondary stage, a state feedback controller based on dynamic inversion is developed which determines the amount of voltage to be monitored across MR damper in order to achieve the required force prescribed by the primary controller. MR damper dynamics have been modelled based on Bouc-Wen model. The numerical results show higher additional damping for in-plane motion compared to out-of-plane motion of cable.