The elastic fields about an inclusion having a shape that is slightly perturbed from that of a circular cylinder are calculated. Both the inclusion and the surrounding matrix are assumed to be isotropic linear elastic materials. Two sets of boundary conditions are applied at the inclusion matrix interface. The first set, corresponding to a coherent interface, consists of balance offorces and continuity of displacement at the interface. The second set, corresponding to a "greased" or incoherent interface, consists of balance of forces, continuity of the component of displacement normal to the interface, and vanishing tangential forces at the interface. Differences between the elastic fields calculated for these two sets of boundary conditions are manifested only in terms which are first order in the amplitude of the shape perturbation. For coherent boundary conditions, the trace of the stress tensor is zero in the matrix and constant in the inclusion when the matrix and inclusion have equal shear moduli. For "greased" boundary conditions, the trace of the stress tensor is generally not constant in either the matrix or the inclusion, even when their shear moduli are equal. The importance of the perturbed elastic fields in relation to morphological stability theory is illustrated by using a constitutive relation for diffusion that depends, in part, on the gradient of the trace of the stress tensor.