  In the article, new asymptotic approximation of the $n$th order is obtained
and proposed to be used in calculations of radiation propagation without
scattering in optically thick media; the asymptotic approximation is much
simpler and more precise than the known diffusion approximation. The rigorous
derivation of the diffusion approximation equation and the equation of the
radiation heat conduction approximation is obtained from the constructed
asymptotic solution of the kinetic equation of radiation propagation in
optically thick media. It is shown, that for optically thick media the
asymptotic solution of the kinetic equation of radiation propagation without
scattering is asymptotic expansion of the exact integral solution of that
kinetic equation. Improved boundary conditions, which are essential for
practical application in calculations of radiation propagation, are derived
(for inner boundaries and outer boundaries with vacuum).
