Heat transfer by simultaneous internal conduction and surface radiation is considered for two equal-length thin plates sharing a common edge. The external surfaces of the plates are insulated while the internal surfaces are gray, specular reflectors for thermal radiation. The problem is formulated in terms of a nonlinear integrodifferential equation which is converted to an integral equation and then solved numerically. Solutions have been obtained for a wide range of conditions including those for which diffuse reflection results are available. Temperature and local heat loss distributions as well as total heat loss calculations are presented and compared with those for diffuse reflectors. Temperatures are lower while local and total heat loss are greater for specular reflection than for diffuse reflection. With applications to radiating fins of rectangular profile in mind, fin effectiveness for specularly reflecting fins are presented and compared to the results for diffuse reflection. The effectiveness of specularly reflecting fins is greater than that of diffusely reflecting fins.