Three methods of increasing exactness are given for calculating the radiant exchange within a multisurface enclosure made up of “real” surfaces. The first approximation considers the directional characteristics of the thermal radiation properties but does not include specular interreflections. The second method incorporates an approximation for specular reflection as well as the directional behavior of real materials. Solutions of the radiant exchange within an enclosure by these two methods are shown to be no more complex than existing techniques for perfectly diffuse enclosures [1, 2]. The third approximation, while more exact, involves a more detailed but not impractical method of solution. Comparisons of the three approximations to the nondirectional diffuse and specular computational methods [8, 9] are presented, and the importance of considering the directional characteristics of thermal radiation properties is shown.