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In this work, four waste paper composites were studied in terms of several photon interaction parameters over the energy region from 0.015 to 15.0 MeV. The waste paper and natural rubber (WP/NR) composites of different densities ranging from ρ = 0.894 to 1.16 gm⋅cm-3 were used for shielding radioactive rubble at different time period stages. Some additives were also used including high-abrasion furnace black, paraffin wax, B4C, as well as magnetite. The deduced parameters of photon interaction: equivalent atomic number Zeq, exposure buildup factor and energy absorption buildup factor have been studied as a function of incident photon energy, WP/NR elemental composition, and for penetration depths, up to 40 mean free path. The Zeq numbers have shown slight variation over the selected incident energy range and buildup factors were found to be modest at low and high photon energy meanwhile their values increase widely over the intermediate energy region. In addition, kerma relative to air for photon energies from 1 to 20 MeV were computed and show dependence upon equivalent atomic numbers. In this work, it was clear that filled samples offer better shielding capabilities than unfilled ones. The obtained data could be useful for radiation physicists and scientists in estimating the γ-irradiation received after applying such shields.