Geant4 simulations and several theoretical approaches such as WinXCOM and ESTAR were used in this work to understand the role of heavy metal oxides on the radiation attenuation features of newly developed TBBE-X glasses which are in the form of 19.5TeO(2)-30B(2)O(3)-30BaO-0.5Er(2)O(3)-20X. Here X stands for SrO, Al2O3, CdO, ZnO, PbO and Bi2O3. According to X (modifier oxide), the glass samples were labelled as TBBE-S, TBBE-A, TBBE-C, TBBE-Z, TBBE-P, and TBBE-B. Various attenuation features such as mass attenuation coefficient (MAC), buildup factors, equivalent and effective atomic numbers, half value layer (HVL), and neutron cross section were investigated. The inclusion of high atomic number and dense atoms in the modifiers (PbO and Bi2O3) in TBBE-P and TBBE-B explains why the energy for the onset of increment in MAC was earliest among the investigated glasses. At a photon energy of 15 keV, HVL of TBBE-S, TBBE-A, TBBE-Z, TBBE-C, TBBE-P, and TBBE-B were 4.67, 5.02, 4.40, 3.91, 3.53, and 3.31 cm respectively. It is found that the TBBE-X glasses have promising shielding properties against gamma radiation comparing to different species of commercial glasses and concrete. The outcomes also reveal that the TBBE-X specimens are comparatively better shields against fast neutron compared to classical shields like graphite, water, and ordinary concrete. Therefore, the TBBE-X glasses have promising shielding properties and can be applied in shielding applications against gamma rays and neutrons beam.