Current methodologies used for the inference of thin film stresses through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film_{strate system. These methodologies have recently been extended to non-uniform stress and curvature states for the thin film subject to non-uniform, isotropic misfit strains. In this paper we study the same thin film}substrate system but subject to non-uniform, anisotropic misfit strains. The film stresses and system curvatures are both obtained in terms of the non-uniform, anisotropic misfit strains. For arbitrarily non-uniform, anisotropic misfit strains, it is shown that a direct relation between film stresses and system curvatures cannot be established. However, such a relation exists for uniform or linear anisotropic misfit strains, or for the average film stresses and average system curvatures when the anisotropic misfit strains are arbitrarily non-uniform.