The impact of TeO2 on the elastic and radiation shielding properties of phospho-tellurite glasses doped with varying amounts of Sm2O3 has been studied. The elastic properties, such as packing factor, packing density, Young’s modulus, bulk modulus, shear modulus, and Poisson’s ratio, were determined by using the Makashima-Mackenzie and Rocherulle models. The gamma-ray shielding parameters, such as mass attenuation coefficient, half-value layer, tenth-value layer, effective atomic number, equivalent atomic number, exposure buildup factor, and energy absorption buildup factor, were calculated using Phy-X/PSD software in the energy range from 0.015 to 15 MeV at penetration depths up to 40 mean free paths for selected glasses. The fast neutron removal cross section was also determined using Phy-X/PSD software. The results show that the mass attenuation coefficient decreases with increasing photon energy but is not influenced by the addition of Sm2O3. The exposure buildup factor values and energy absorption buildup factors have lower values in the low- and high-energy regions and higher values in the intermediate energy region. The 1.5 mol % concentration of Sm2O3 in the selected glass shows higher exposure buildup factor and energy absorption buildup factor values in the intermediate energy region. Among the selected glasses, PZBTS1.5 has the highest value of fast neutron removal cross sections. The high density, high effective atomic number, and transparency to visible light of these materials indicate that they can be used as shielding materials in nuclear reactors and nuclear technology.