A system that consists of a misfit precipitate transforming from an infinite matrix is analyzed to determine the effect of elastic fields on a morphological stability analysis. Elastic fields enter the analysis through the boundary condition that sets the solute concentration at the interphase interface. Elastic fields influence the stability results when the shear modulus of the precipitate is different from that of the matrix; they act to stabilize the interface and favor spherical growth shapes if the shear modulus of the precipitate is greater than that of the matrix, and to destabilize the interface and favor non-spherical growth shapes in the alternative case. These elastic effects are especially pronounced at small supersaturations. For the case of a hard precipitate growing in a soft matrix, elastic fields can, at small supersaturations, absolutely stabilize the interface against any given perturbation wavelength. In the absence of capillarity, elastic fields spoil the shape preserving growth of an ellipsoidal precipitate, a solution found by Ham when both capillarity and elastic fields vanish. When a precipitate is undergoing unstable growth, elastic fields shift the value of the fastest growing harmonic such that stabilizing elastic fields favor long wavelength perturbations and relatively smooth growth shapes, while destabilizing elastic fields favor short wavelength perturbations and relatively rough growth shapes.