Symmetrization of the radiation field by multiple absorption and re-emission in hohlraum targets for indirectly driven inertial confinement fusion (ICF) is investigated. The radiation field on the confining wall and on the fusion capsule is calculated self-consistently, taking into account the angular distribution of the X-rays received and emitted by each surface element. Wall physics are described by approximate ablative heat wave relations, giving the absorbed flux, the temperature and the thermally re-emitted flux for each wall element. Hydrodynamic motion is not taken into account. Concerning the geometrical design, different cases of interest for heavy ion drivers are presented. It is shown that capsule illumination with 1–2% non-uniformity can be obtained with two-sided beam/X-ray conversion; single-sided drive seems not to be practicable. Symmetrization versus transfer efficiency is discussed as a function of area ratio.