We investigate the free-edge stresses in anisotropic bimaterials through the use of the free-edge stress intensity factor, Kf. This requires a determination of the singularity order at the free-surface as well as a calculation of the near-field stresses. We determine the order of the singularity for arbitrary free-surface orientation of the upper material using an eigenvalue analysis for anisotropic bimaterials. The interfacial stresses are determined using a boundary element calculation based on anisotropic, bimaterial Green's functions. The variation of Kf with free-surface orientation is determined. We find that the free-edge singularity vanishes for certain angles dependent on the anisotropic elastic constants.