Polymer composites reinforced with heavy metals have wide applications in the nuclear industry as radiation shielding materials against emitted radiation from nuclear equipment. In this study, considering bismuth oxide as reinforcement, various polymers including thermoplastic polymers, such as high-density polyethylene, low-density polyethylene, polypropylene, polyvinyl acetate, polymethyl methacrylate, and thermosetting epoxy resin have been considered as matrices. After preparing various samples of polymer composites loaded with 60 % by weight of bismuth oxide, some physical, mechanical, and radiation shielding properties (neutron and gamma attenuation coefficients) of these polymer composites have been measured and compared with each other. First, the density of the samples was measured, and the response of these samples to varying compressive force was investigated. The stress-strain diagrams of composites with different matrices were compared. Subsequently, the linear and mass attenuation coefficients of the composites were measured over a wide range of energies (32–1480 keV) against direct and collimated beams from various standard gamma-ray sources (134Cs, 60Co, 154Eu, 133Ba, and 22Na) using an HPGe detector. A collimated beam from an Am–Be source was utilized to measure and compare the attenuation properties of the composite samples against neutron flux. Furthermore, the properties of the composites against neutron and gamma radiation were calculated using the MCNP Monte Carlo code over a broad energy range, and the results were compared and validated with the experimental data. The comparison of the calculated and measured results shows reasonable agreement. The results indicate that in situations where high attenuation properties coupled with high strength are desired, polymeric composites with an epoxy matrix can be considered as radiation shielding materials. If the use of flexible and malleable material is required, such as for reactor piping shielding or the fabrication of protective gloves and clothing in a radiation environment, among the polymers studied, polyvinyl acetate is a more suitable matrix.