Abstract: Predicting the shape of a critical nucleus in solids has been a long-standing problem in solid-state phase transformations. We show that a diffuse-interface approach together with a minimax algorithm is able to predict the critical nucleus morphology in elastically anisotropic solids without a priori assumptions. We demonstrate the possibility of nonconvex surfaces for critical nuclei. It is found that strong elastic energy contributions may lead to critical nuclei whose point group symmetry is below the crystalline symmetries of both the new and the parent phases.