The effect on radiation distributions in heterogeneous multilayer shield configurations containing cylindrical air-filled voids of different diameters have been investigated. The heterogeneous shield assemblies were placed in front of one of the horizontal channels of the ET-RR-1 reactor. The measurements of δ-rays and slow neutrons were carried out using LiF-7 and LiF-6 Teflon disc dosimeters, respectively. It was found that the presence of air-filled voids increases the radiation along and perpendicular to the void axis. An empirical formula has been derived to calculate the radiation distribution in the multilayer shields and a good agreement between the measured and calculated values was obtained. The formulae developed by Chase have been checked experimentally to determine the minimum amount of “patching” required on the outside of the voided shields to maintain a uniform emergent radiation distribution on the outer surface of the shielding assembly. The applicability of this formula has been defined and a semi-empirical formula developed to describe the experimental results obtained for the required “patching”.