The mineral zircon has particular geological significance because of its use in the age determination of rocks and as a structural analogue phase for radioactive waste forms. Despite its widespread utility, however, radiation damage of the crystal structure (metamictization) causes a volume expansion of the crystal lattice and the generation of internal stresses which can induce fractures in the crystal. A model has been developed which describes the state of stress in n concentric spherical shells, each of which may have different material properties; the case of a three-shelled composite sphere has been examined explicitly. In combination with fracture mechanics theory, the model predicts that spatially distinct radial and/or concentric fracture sets can be produced, and such fracture patterns accurately describe the distribution and types of self-induced fractures observed in natural zircons. In general, the formation of such microfractures in zircon is a function of the degree of metamictization, shell thickness, and the confining pressure. The model predicts that the maximum depths in the Earth's crust at which radial versus concentric fractures can form in a crystal are different, suggesting that the types of fractures found in a suite of zircons from a particular rock might be potential indicators of the depth of burial. Because metamictization-induced fractures may serve as potential pathways for the rapid leaching of various elements from the zircon crystal, this may also have important implications in interpreting the U/Pb ages of fractured zircons or in evaluating the suitability of related crystalline phases as hosts for nuclear waste.