An excellent vortex suppression device, in the form of an antinode fairing is presented towards reducing the Vortex Induced Vibration of structural members exposed to flow. An analytical procedure is also developed to optimise the depth and location of the fairings along the members. Two newly developed fairing sections are tested on cylindrical legs of a Jackup model and the results are qualitatively compared with the expected behaviour, particularly the effect of selected fairlead depth and location. A simplified mathematical model is developed based on the principle of conservation of energy, which could be used to decide the optimum location and depth of the vortex suppression devices for the cylinders undergoing Vortex Induced Vibration in a uniform flow. Based on the mathematical studies, modal antinodes are found as the optimum locations for the installation of the fairings and accordingly two compact leg fairing designs have been developed for practical applications. Those are based on NACA0018 profiles but with reduced L/B ratios of around 2.40 and 3.00. The tests with scaled down Jackup models with cylindrical legs demonstrated that both the fairing designs could reduce Vortex Induced Vibration amplitudes significantly, by around 80%. The weathervaning stability of both the fairing designs were also found to be satisfactory. From the mathematical studies and test results, it is inferred that fairings contribute to the reduction of Vortex Induced Vibration in three ways; reduction of excitation force, disruption of vortex synchronisation and the increase in fluid damping. Fairings are also found not to have significant bearing on the drag coefficient of the structure. The fairing design with the lesser L/B ratio of 2.40 is found to be an optimal solution for vortex suppression, when the structure is not sensitive to drag forces. However, fairings are found to initiate galloping responses at higher flow speeds above the lock-in range and hence it is recommended that the same shall be of the detachable type for cylinders exposed to large flow speed variations. The mathematical approach presented will enable practicing engineers to design and optimise antinode fairings for structures experiencing Vortex Induced Vibration. The two fairing section offsets presented may be readily used by Industry for practical applications.