In this paper an advanced modeling approach is employed to investigate the development of surface Kelvin-Helmholtz instability, occurring at liquidliquid interfaces. The interface is captured by the Level-Set method, in which, the interface is represented as the zero level set of a smooth function. A high-order numerical scheme, called Var-Den , is utilized to solve the Navier-Stokes and the Level-Set equations with high accuracy. The sensitivity analysis is performed to identify important factors, governing the interfacial interactions and the interface evolution behavior. In particular, the effect of surface tension to viscosity forces ratio, i.e. Ohnesorge number, on the surface instability development is examined. The simulation results show that the advanced simulation approach, based on the level-set method, is a useful and promising method to gain insight into micromechanics of surface instabilities. It is found that viscous dissipation has a significant influence on the evolution of the instabilities on the liquidliquid interface. Three distinct evolution regimes, depending on the Weber and Ohnesorge numbers, are identified, namely the oscilatory regime, the fingering regime, and the roll-up regime. Advances in Fluid Mechanics III, C.A. Brebbia & M. Rahman (Editors) © 2000 WIT Press, www.witpress.com, ISBN 1-85312-813-9 426 Advances in Fluid Mechanics III