Abstract: The evolution of material interpenetration boundary induced by Rayleigh-Taylor instability is calculated under various acceleration histories and density ratios using a buoyancy-drag model, which reveals that the mixing development under a constant acceleration is very different from that under a variable acceleration, and that the asymmetry between a bubble and a spike enhances with the increase of the density ratio. The calculation results are compared with detailed experiment data to prove the validation of the choice of model constants, the addition of phenomenal ratio factors and model assumption used. These results provide theory guides for applying a buoyancy-drag model to related engineering designs directly and for replacing existing empirical expressions, which greatly promote the development of engineering fields related to mixing phenomenon induced by instabilities.