Polycrystals are aggregates of numerous tiny crystallites whose orientation distributions are described by the orientation distribution function (ODF). Since crystal lattices are anisotropic, the properties of polycrystals depend on the ODF. The texture coefficients, which can be measured by X-ray diffraction, are the expanded coefficients of the ODF under the Wigner D -function bases. The texture coefficients contain the information of crystalline orientation distributions and crystal symmetries on polycrystals. Herein an orientation-dependent function is introduced to present the properties of polycrystals. A general expression of the orientation-dependent function for polycrystals is given. The general expression with the texture coefficients can be widely used to determine the properties of polycrystals. As applications of the general expression, the direction-dependent function, the elastic strain energy, and the yield function for anisotropic cubic polycrystals are given in simple and explicit forms.