The first principles calculations based on density functional theory are performed to investigate the anisotropies of four superhard materials (w-BN, w-BC2N, r3m-BC2N, and r3m-B2CN).By calculating Poissons ratio, we found that the atomic binding forces of the first three materials are non-central forces,whereas that of r3m-B2CN is a central force.According to the elastic percentage anisotropy (AB, AG, and AE) and the calculated values of shear anisotropic factor A, the four materials are proven to have elastic anisotropy.Moreover, the different shapes in the three-dimensional stereograms of Youngs modulus on all surfaces, as well as the tensile and shear stress-strain curves in different crystal orientations can further account for the anisotropies of these materials.In addition, the anisotropic factors of acoustic wave and thermal conductivities in the propagation directions of [0001] and (0001) are also calculated.w-BN,w-BC2N, and r3m-BC2N have similar calculated values, which explain why they have similar properties.By contrast, r3m-B2CN has a large degree of anisotropy, and the three-dimensional diagram of its Youngs modulus has an "8" shape.