The stress driven growth of an expanding precipitate at a crack tip is studied. The material is assumed to be linearly elastic, and the expansion is considered to be isotropic or transversely isotropic. The extent of the precipitate is expected to be small as compared with the crack length and distance to boundaries. The problem has only a single length scale given by the squared ratio of the stress intensity factor and a critical hydrostatic stress that initiates the growth of the precipitate. Therefore, the growth occurs under self-similar conditions. The equations on non-dimensional form show that the free parameters are expansion strain, degree of anisotropy and Poisson's ratio. It is found that the precipitate, once initiated, grows without remote load for expansion strains above a critical value. The anisotropy of the expansion strongly affects the shape of the precipitate but does not have a large effect on the crack tip shielding.