We have shown in a series of recent papers that the classical theory of elasticity can be extended to the nano-scale by supplementing the equations of elasticity for the bulk material with the generalized Young-Laplace equations of surface elasticity.This lecture shows how this has been done in order to capture the mechanical properties of nano-structured particulate and porous materials.It begins with a description of the generalized Young-Laplace equations.It then generalizes the classical Eshelby formalism for nano-inhomogeneities; the Eshelby tensor and stress concentration tensor now depend on the size of the inhomogeneity and the location of the material point in it.Then two applications of the Eshelby formalism for nano-inhomogeneities are presented, which include calculations of the elastic fields in core-shell nanoparticles and quantum dot (QD) structures.