This paper studies the diffusion of stresses in a linear isotropic elastic body coated with a thin elastic shell called the «crust». Two static problems are considered. The first is that of the semi-infinite half-space covered by a thin plate subject to a point load at the origin. In the second problem a solid elastic sphere enveloped by a thin spherical elastic shell with two opposite point loads at the poles is investigated. Solutions for the displacement within the thin crust are obtained in the two problems by means of the Hankel transform and the Legendre polynomial respectively. © 1985 Pitagora Editrice Bologna.