The diffusion-controlled growth of a spherical particle embedded in a solid matrix of infinite size has been theoretically investigated for binary alloys, in the framework of the diffusion-under-stress formalism developed by Cahn-Larché. Assuming a composition stress develops in the particle, both concentrations of the diffusing species have been determined in the particle and in the matrix, as well as the interface velocity. The dependence on the composition stress and heterogeneous shear moduli of the concentrations in the particle and the interface growth rate has been characterized.