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Researchers have tested the potential of various polymer composites for use in radiation shielding. They are light and non-toxic compared to lead and have potential as shielding in the nuclear industry where mixed fields of neutron and gamma radiation are encountered. Despite the widespread use of polymers in the last decade, more data is needed on the shielding properties of the wide range of polymer composites doped with different high atomic-number constituents. Using polymer composites for ionising radiation attenuation and shielding applications requires empirical investigation before achieving commercial viability. The objectives of this study are to prepare concrete radiation shielding with different formulations, study the neutron dose transmission measurement, and simulate the attenuation properties of neutron and gamma. This research will attempt to use waste plastics to make a novel WPIC mix for gamma and neutron radiation shielding purposes. These mixes are achieved by the simultaneous incorporation of waste polymeric material and high-density fine and coarse aggregate components from the iron industry in place of conventional ingredients. The results have indicated that the waste plastics, along with by-products of the iron industry, can be conveniently used to make concrete mixes with acceptable compressive strength characteristics and significantly enhanced shielding capabilities with respect to gamma and neutron radiations. In the back-drop of disposal of the ever-increasing volumes of plastic waste becoming a major environmental issue in both developed/developing economies, recycling such plastic wastes as a possible construction material, as attempted herein, appears to be the viable solution towards the pollution problem. Additionally, large quantities of waste plastics are consumed without compromising the structural requirements.