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A new, general-purpose computer program (BIFAC) has been developed for computing thermal radiant interchange among opaque surfaces that need not be perfectly diffuse or perfectly specular. The method uses the full bi-directional reflectance distribution function (BRDF) to determine directional radiosities, and thence heat fluxes, between surfaces. The method gives more accurate average interchange factors for diffuse surfaces, because it better represents interaction in corners. The maximum error in a stringent test using a specular surface was 8.9%, in great part because the exact specular solution does not include the real specular cone that is used in BIFAC.