High order weighted essentially non-oscillatory finite difference schemes (FD-WENO) are applied successfully to numerical simulation of gravity-driven high density ratio Rayleigh-Taylor instability problems and laser ablative Rayleigh-Taylor instability problems in two dimensions. It provides important references to numerical study of inertial confinement fusion (ICF) as well as to other high-tech fields. High order FD-WENO schemes are applicable to numerical simulation of ICF inplosion.