The radiative transfer equation (RTE) has been modeled by using hybrid double and octuple spherical harmonics approximations for one-dimensional plane-parallel and two-dimensional cylindrical geometrics, respectively. The governing equations for these approximations are systems of first-order partial differential equations. In the formulation for the one-dimensional case, a linearly anisotropic scattering phase function is used, whereas, for the two-dimensional case, a delta-Eddington phase function is employed. Emitting and diffusely-reflecting boundaries are considered. Numerical solutions of the equations for the plane-parallel geometry are obtained using a software package DISPL2 and the results are compared with those available in the literature.