Abstract
The boundaries of stability are determined for the Rayleigh-Taylor instability at a cylindrical interface between an ideal fluid in the interior and a heavier elastic-plastic solid in the outer region. The stability maps are given in terms of the maximum dimensionless initial amplitude ξ_{th}^{*} that can be tolerated for the interface to remain stable, for any particular value of the dimensionless radius B of the surface, and for the different spatial modes m of the perturbations. In general, for the smallest dimensionless radius and larger modes m, the interface remains stable for larger values of ξ_{th}^{*}. In particular, for m>1 and B→0, it turns out ξ_{th}^{*}→1, and a cylindrical geometry equivalent to Drucker's criterion is found, which indeed ends up being independent of the interface geometry.
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