  We derive the incremental equations for a hyperelastic solid that incorporate
surface tension effect by assuming that the surface energy is a general
function of the surface deformation gradient. The incremental equations take
the same simple form as their purely mechanical counterparts and are valid for
any geometry. In particular, for isotropic materials, the extra surface elastic
moduli are expressed in terms of the surface energy function and the two
surface principal stretches. The effectiveness of the resulting incremental
theory is illustrated by applying it to study the Plateau--Rayleigh and Wilkes
instabilities in a solid cylinder.
