Abstract.  In inertial confinement fusion (ICF) experiment ablatively driven shocks is an important phenomena for studding equation of state of solids. The interface between two fluids becomes unstable when driven by impulsively acting force, e.g., gravity. In the former case it is called Richtmyer-Meshkov (RM) instability and Rayleigh-Taylor (RT) instability in the latter case. In the nonlinear stage the fluid interface is found to develop structures having finger like shapes. The structure resembles a bubble (spike) according as lighter (heavier) fluid pushes in to heavier (lighter) fluid. The dynamics of interfacial instabilities have been studied for several cases. It has shown that the instability can be mitigated under certain condition applicable in Inertial Confinement Fusion as well as astrophysical experiment on intense lasers.