The surface tension of liquid metals is an important and scientifically interesting parameter which affects many metallurgical processes such as casting, welding and melt spinning. Conventional methods for measuring surface tension are difficult to use for molten metals above temperatures of 1000 K. Containerless methods are can be used to measure the surface tension of molten metals above 1000 K. Oscillating drop method is one such method where a levitated droplet is allowed to undergo damped oscillations. Using the Rayleigh’s theory for the oscillation of force-free inviscid spherical droplets, surface tension and viscosity of the sample can be calculated from oscillation frequency and damping respectively. In this thesis, a numerical model is developed in ANSYS Fluent to simulate the oscillations of the molten metal droplet. The Volume of Fluid approach is used for multiphase modelling. The effect of numerical schemes, mesh size, and initialization boundary conditions on the frequency of oscillation and the surface tension of the liquid are studied. The single-phase model predicts the surface tension of zirconium within a range of 13% when compared to the experimental data. The validated single phase model is extended to predict the interfacial tension of a core-shell structured compound drop. We study the effect of the core and shell orientation at the time of flow initialization. The numerical model we developed predicts the interfacial tension between copper and cobalt within the range of 6.5% when compared to the experimental data. The multiphase model fails to provide any conclusive data for interfacial tension between molten iron and slag.