This paper describes the application and comparison of three Discrete Ordinates Methods: the Discrete Ordinates Interpolation Method (DOIM) for structured and unstructured grids; the Discrete Ordinates Method in Orthogonal Curvilinear Coordinates (DOM-OCC) for structured grid; and the Discrete Ordinates Method associated to the Finite Volume method and Ray Tracing (DOM-FV-RT) for unstructured grid. A summary of the basic equations and numerical formulations is given for each method to outline their key characteristics. In order to extract valuable information to improve DO kind methods when applied to complex geometries, they are compared in the case of radiative equilibrium of a gray medium confined between infinite black or diffusely reflecting circular or elliptical cylinders. For the circular ring problem, the three DOMs results are confronted with Monte Carlo ones for various radius ratios and radiative properties. The elliptical ring problem extends the comparison to a more complex geometry and an emphasis is put on the evaluation of wall radiation fluxes, In conclusion, distinctive features in terms of performances are observed for each method. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.