Special types of concrete radiation shields that depend on locally available materials and have improved properties for both neutron and gamma-ray attenuation were developed by using plastic materials and heavy ores. The analytic hierarchy process (AHP) is implemented to evaluate these types for selecting the best biological radiation shield for nuclear reactors. Factors affecting the selection decision are degree of protection against neutrons, degree of protection against gamma rays, suitability of the concrete as building material, and economic considerations. The seven concrete alternatives are barite-polyethylene concrete, barite-polyvinyl chloride (PVC) concrete, barite-portland cement concrete, pyrite-polyethylene concrete, pyrite-PVC concrete, pyrite-portland cement concrete, and ordinary concrete. The AHP analysis shows the superiority of pyrite-polyethylene concrete over the others.