Abstract: Radiative transfer is the main phenomenon in the basis of several relevant problems of scientific and technological interest. Examples of application of the mathematical and computational modelling of such phenomenon can be found in astronomy, environmental sciences, engineering and medicine among many different areas. The integro-differential equation known as Boltzmann equation describes mathematically the interaction of the radiation with the participating medium, i.e. a medium which can absorb, scatter and emit radiation. Several methods have been developed for the solution of the Bolztmann equation. In the present work we present a comparison of the solutions obtained for the one-dimensional problem with four different methods: (i) a Monte Carlo (MC) method; (ii) the Discrete Ordinates method (SN) combined with a finite difference approximation; (iii) the Analytical Discrete Ordinates method (SNA); and (iv) the Laplace Transform Discrete Ordinates Method (LTSN). Our final objective is to solve the inverse radiative transfer problem and for that purpose we want to investigate methods that can provide accurate and fast solutions for the direct problem.