The elastic fields about an inclusion having the shape of a sphere perturbed by a spherical harmonic are calculated by using isotropic linear elasticity theory. This shape is chosen in order to facilitate coupling of this problem with a morphological stability analysis. The components of the displacement field u(r, θ, φ) about the inclusion are found to be proportional to the components of the gradient of the perturbing harmonic. Two alternative boundary conditions are considered, corresponding to 1. (1) a coherent interface, in which forces and displacements are continuous across the interface 2. (2) a "greased" interface, in which forces tangential to the interface vanish at the interface. For a coherent interface, the sign of the dilatation in the matrix depends on the ratio of the shear moduli of the inclusion and matrix; whereas for a greased interface, the sign of the dilatation in the matrix is independent of this ratio. Also, for a greased interface, the perturbation affects the dilatation in the inclusion; this is not the case for a coherent interface.