The diffusion-controlled dissolution of a spherical particle consisting in two epitaxially stressed solid phases of a substitutional binary alloy in contact with an undersaturated solution is investigated. A linear stability analysis of the solid-liquid interface demonstrates that a morphological instability of the particle may occur due to the epitaxial stress generated by the spherical precipitate embedded in the solid matrix, the liquid pressure being neglected. The critical radius of the particle below which the interface is unstable is determined and the conditions for the roughness development are discussed.