The work reported here was undertaken to find algebraic equations for the preferred habits of coherent thin-plate inclusions in anisotropic media on the assumption that the inclusion and matrix can be treated as linear elastic continua. The preferred habit minimizes the elastic energy, which depends on the elastic constants of the inclusion and the transformation strain connecting the lattices of the inclusion and the matrix. The paper presents four principal results concerning the preferred thin-plate habit. First, the mathematical conditions that determine the preferred habit are derived in compact form. Second, it is shown that these conditions are always satisfied when the transfo~ation strain is dyadic and the habit is perpendicular to a vector of the dyad, reproducing a result that is given by Khatchaturyan and included in the "crystallographic theory" of precipitate habits. Third, the extremal conditions are solved for orthorhombic symmetry, that is, when the elastic constants of the inclusion have orthorhombic symmetry with respect to the principal axes of the transformation stress. The results incorporate isotropic, cubic, hexagonal and tetragonal (type II) symmetries. They are specialized to determine the minimumenergy habit as a function of the transfo~ation strain for three classes of inclusions: isotropic inclusions, cubic inclusions with tetragonal transformation strains, and hexagonal inclusions with hexagonal transformation strains. Finally, it is shown by counter-example that there is no general algebraic solution for systems of arbitrary symmetry.