We perform the analysis of the Rayleigh–Taylor instability of thin perfectly elastic solid plates using the analytical approach recently developed by Piriz and coworkers. The model describes the evolution of the perturbation amplitude from the initial conditions and at relatively long times it yields the asymptotic growth rate. It applies to solid/inviscid fluid interfaces. For the particular case of solid/vacuum interface, the model has been compared with the exact results by Plohr and Sharp and an excellent agreement has been found. In general, thinner plates are found to be more unstable and, in the presence of a fluid below the elastic plate, the growth rate is reduced.

Numerical simulations of the Rayleigh-Taylor instability in the interface of two semi-infinite media have been performed based on the finite element method. Two different interfaces have been considered: elastic solid/elastic solid and elastic solid/viscous fluid. The results have been compared with previously published analytical models. In particular, the asymptotic growth rate has been compared with the model by Terrones (2005) while the initial transient phase is compared with the model by Pirizet al.(2005). Finally, some examples show the importance of such an initial transient phase if more realistic material laws (for example, elastoplastic behavior) are taken into account.