We have developed a theoretical framework for the computation of the transfer of solar radiation in an anisotropic medium with particular application to oriented ice crystals in cirrus clouds. In the theoretical development, the adding principle for radiative transfer has been used with modifications to account for the anisotropy of the phase matrix. The single-scattering properties including the phase function, single-scattering albedo, and extinction cross section, for randomly and horizontally oriented ice crystals are then used in the computation of reflected and transmitted intensifies, planetary albedo, and polarization in multiple scattering. There are significant differences in the reflected and transmitted intensifies between hexagonal ice crystals and equivalent ice spheres. In addition, it is found that ice spheres are inadequate to model the general pattern of reflected intensity. The orientation properties of ice crystals are also significant in the determination of the reflected and... Abstract We have developed a theoretical framework for the computation of the transfer of solar radiation in an anisotropic medium with particular application to oriented ice crystals in cirrus clouds. In the theoretical development, the adding principle for radiative transfer has been used with modifications to account for the anisotropy of the phase matrix. The single-scattering properties including the phase function, single-scattering albedo, and extinction cross section, for randomly and horizontally oriented ice crystals are then used in the computation of reflected and transmitted intensifies, planetary albedo, and polarization in multiple scattering. There are significant differences in the reflected and transmitted intensifies between hexagonal ice crystals and equivalent ice spheres. In addition, it is found that ice spheres are inadequate to model the general pattern of reflected intensity. The orientation properties of ice crystals are also significant in the determination of the reflected and...