Collection efficiencies are determined for integrating hemi-ellipsoids and integrating hemispheres used in connection with radiation surface property measurements. The Monte Carlo method is employed to simulate the trajectories of photon bundles which leave a source of radiation and are collected and focused onto (or adjacent to) a receiver. The radiation source may be a test surface whose reflectance or emittance is to be determined, while the receiver may be a radiation detector. Results are obtained for a wide range of source and receiver sizes and positions. The results show that in the case of the hemi-ellipsoid, the attainment of good collection efficiency requires that the radius of the receiver be at least twice that of the source. The hemisphere is, in general, a less efficient collector than the hemi-ellipsoid When the source and receiver are only slightly displaced from the center of the base plane circle of the hemisphere, then the two collectors are comparably efficient.