A new model and code for radiative heat transfer based on the numerical solution of the radiative transfer equation by finite volume method in 3-D Cartesian coordinates coupled with weighted sum of gray gases model (WSGGM) is developed. The Smith's WSGG model with 4 and 5 gray gases is used, but any other gas radiative properties model can be incorporated. The physical and mathematical concepts of the model are presented in details. The series of calculations for real gases as water vapor and a mixture of carbon dioxide, water vapor and nitrogen for uniform and non-uniform temperature fields are carried out. The predictions are compared against the rare results found in literature. The results calculated by ray tracing method with statistical narrow band model, recently published, were taken as the benchmark. The agreements with them are very good. The effects of spatial rectangular grids, of angular discretization in polar and azimuthal directions and of number of gray gases on the accuracy were analyzed. Also a new series of predictions for the mixture of 0.1 of carbon dioxide, 0.1 of water vapor and 0.8 of nitrogen on mole base is performed. It is believed that the mathematical model developed, avoiding the drawbacks of spectral lines and bands models, is sufficiently accurate and convenient for engineering calculations as well as for incorporation in computational fluid dynamics codes. (C) 2003 Elsevier Ltd. All rights reserved.