Consideration is given to the radiant interchange within finite-length cylindrical holes, one end of which is open to the environment. The bounding surfaces of the hole are isothermal and radiate in a gray, diffuse manner. The problem is analyzed by applying radiant flux balances to infinitesimal elements of surface, and this gives rise to two simultaneous integral equations. The solutions to these provide such technically interesting results as the distributioti of the apparent emissivity and local heat flux along the bounding surfaces and, also, the over-all heat flux streaming from the hole. It is found, for example, that to achieve an apparent emissivity of 0.99, the minimum length of hole is 1.6, 2.6, or 4 diameters depending on whether the surface emissivity ε is 0.9, 0.75, or 0.5. The over-all heat loss results demonstrate the effect of the presence of pits and depressions in increasing the heat loss frotn a surface.