Development of materials for radiation shielding application, which are lightweight, flexible, and robust increases in demand for nuclear radiation facilities including industrial or medical applications. In this paper, three metals (lead, gadolinium, bismuth) doped polymeric compounds (poly-acrylonitrile, polyethylene, and kevlar) were simulated by using theoretical and computational model. It was assumed that lead, gadolinium and bismuth were dispersed homogenously. Both theoretical and computational model were used to calculate the attenuation coefficients of these composite polymeric compounds. At first, theoretical calculations were performed and then computational models were used to simulate the irradiation of the polymeric compounds under various photon energy sources. For each compound, attenuation coefficients were calculated under different percentages and then compared with two computational programs. The work attains novelty as no work is ever reported on the metal/ polymeric composites for radiation shielding applications by theoretical-computational technique. This approach was used for the material selection and estimating the possibility of error and to calculate attenuation coefficients under various radiation doses. The research opens new grounds for developing radiation-shielding materials by computational techniques.