In this manuscript,, we discuss the influence of surface and interface stress on the elastic field of a nanoparticle, embedded in a finite spherical substrate. We consider an axially symmetric traction field acting along the outer boundary of the substrate and a non-shear uniform eigenstrain field inside the particle. As a result of axial symmetry, two Papkovitch-Neuber displacement potential functions are sufficient to represent the elastic solution. The surface and interface stress effects are fully represented utilizing Gurtin and Murdoch’s theory of surface and interface elasticity. These effects modify the traction-continuity boundary conditions associated with the classical continuum elasticity theory. A complete methodology is presented resulting in the solution of the elastostatic Navier’s equations. In contrast to the classical solution, the modified version introduces additional dependencies on the size of the nanoparticles as well as the surface and interface material properties.