The Synthetic Kernel (SKN) approximation is employed to radiative transfer problems of hollow spherical participating and linearly anisotropically scattering medium. The SKN method relies on approximating the integral transfer kernels by synthetic kernels. The radiative integral transfer equations (RITEs) are then reduced to a set of coupled second-order differential equations. The method is tested against exact solution for various optical geometries, constant and space-dependent scattering albedo variations simulating homogencous/inhomogeneous medium. It is demonstrated that low order SKN approximation can be used to solve one dimensional radiative transfer problems of spherical participating medium.