The Synthetic Kernel (SKN) method is applied to a solid spherical absorbing, emitting and linearly anisotropically scattering homogeneous and inhomogeneous medium. The SKN method relies on approximating the integral transfer kernels by Synthetic Kernels. The radiative integral transfer equation is then reducible to a set of coupled second-order differential equations. The SKN method, which uses Gauss quadratures, is tested against integral equation and the discrete ordinates S-8 solutions for various optical radius and scattering albedo variations. (C) 2007 Elsevier Ltd. All rights reserved.