A rotationally symmetric body which is totally immersed in a liquid that co
ntains reactants which dissolve the solid is considered. The body is in a v
ertical position, which means that the heavier liquid close to the body mov
es downwards under the action of the force of gravity. This free-convective
motion creates a concentration field around the body, with the concentrati
on gradient at the surface being proportional to the speed of dissolution o
r etch rate. A special body shape is sought for which the dissolution proce
ss results in a succession of body shapes which are all the same, that is,
the etching process is shape-preserving. It turns out that a fully analytic
al solution describing the body shape can be obtained. The speed at which t
he body moves downwards as a result of etching is proportional to rho(-1/4)
, where rho is the radius of curvature at the body apex. This analytical so
lution is ideally suited as a benchmark against which numerical codes can b
e tested.