Analytic solutions to the three-dimensional infrared radiative transfer equation for an anisotrapic and isothermal scattering cloud layer are derived by utilizing the four-term truncated spherical harmonics expansion for the scattering phase function and intensity. Computational results of the upward and downward intensity and flux density for cubic, rectangular and plane-parallel clouds employing a wavelength of 10 µm are presented and physically discussed. We show that the emissivities of cubic clouds are ∼20–30% lower than the values calculated from the plane-parallel program, and that optically thick cubic clouds cannot be considered as black clouds. Further, we found that cubic clouds undergo much stronger cooling at the top as compared to plane-parallel clouds, Relatively small cooling is also evidenced near the cubic cloud bottom. These computational results and physical findings appear to have significant implications to the interpretation of satellite soundings to inter the cloud-top tem... Abstract Analytic solutions to the three-dimensional infrared radiative transfer equation for an anisotrapic and isothermal scattering cloud layer are derived by utilizing the four-term truncated spherical harmonics expansion for the scattering phase function and intensity. Computational results of the upward and downward intensity and flux density for cubic, rectangular and plane-parallel clouds employing a wavelength of 10 µm are presented and physically discussed. We show that the emissivities of cubic clouds are ∼20–30% lower than the values calculated from the plane-parallel program, and that optically thick cubic clouds cannot be considered as black clouds. Further, we found that cubic clouds undergo much stronger cooling at the top as compared to plane-parallel clouds, Relatively small cooling is also evidenced near the cubic cloud bottom. These computational results and physical findings appear to have significant implications to the interpretation of satellite soundings to inter the cloud-top tem...