The mass attenuation coefficients, μ/ρ, half-value layer, HVL, tenth-value layer, TVL, effective atomic numbers, ZPIeff, and effective electron densities, Ne,eff, of borate glass sample systems of (100-x-y) Na2B4O7 : xPbO : yNiO (where x and y=0, 2, 4, 6, 8, and 10 weight percentage) containing PbO and NiO, with potential gamma ray and neutron shielding applications, have been investigated. The gamma ray interaction parameters, μ/ρ, HVL, TVL, ZPIeff, and Ne,eff, were computed for photon energy range 1 keV–100 GeV. The macroscopic fast neutron removal cross-sections (ΣR) have also been calculated. Appreciable variations were noted for all the interaction parameters by varying the photon energy and the chemical composition of the glass samples. The better shielding properties of borate glass samples containing PbO were found. These results indicated that borate glass samples are a good radiation shielding material.