A detailed analysis has been made to obtain both physical insight and numerical results for radiation between gray surfaces. In particular, it was desired to examine the common assumption that the incident radiation is uniformly distributed over a surface. To lift this assumption, the radiation problem must be formulated in terms of integral equations. The study was carried out for two simple configurations: Two plates sharing a common edge, and two parallel plates. Solutions of the governing integral equations were found for a wide range of geometric and radiative conditions. A detailed interpretation is made of the results, and comparisons with the predictions from the simplified theory of uniform incident radiation are presented.