Abstract: In the numerical simulation of the interfacial instability, the schemes in 1,4~8 were limited probiems in one medium with different densities or two media with homologous adiabatic exponent.If the schemes are used in computing the disturbance of different medium interfaces with homologous adiabatic exponent, the physical guantities on interfaces may give rise to nonphysical oscillation.To overcome the problem, this paper introduces the front tracking scheme ² into the Level Set method, name y the contact discontinuous boundary conditions are coercively added on interfaces so that the nonphysical oscillation is avoided.The evolution of Rayleigh-Taylor instability is examined by the three-dimensional TVD/AC program under the single wave.The disturbed figures with time are given.