A linear study of the Rayleigh–Taylor instability based on momentum conservation and the
consideration of an irrotational velocity field for incompressible perturbations is discussed. The
theory allows for a very appealing physical picture and for a relatively simple description of the
main features of the instability. As a result, it is suitable for the study of the very complex
problem of the instability of accelerated solids with non-linear elastic–plastic constitutive
properties, which cannot be studied by the usual normal modes approach. The elastic to plastic
transition occurring early in the instability process determines the entire evolution and makes the
instability exhibit behavior that cannot be captured by an asymptotic analysis.