A melt quenching method has been used to prepare xBaO-30Bi(2)O(3)-(70-x)B2O3 and xZnO-30Bi(2)O(3)-(70-x)B2O3 glasses, where 5 <= x <= 30 mol. %. The mass attenuation coefficients (MAC) for the prepared glasses have been calculated using MCNPX (version 2.6.0) Monte Carlo code in the energy range 0.122-1.33 MeV and the results have been compared with those obtained by XCOM program. From the obtained MAC, different shielding parameters such as effective atomic number (Zeff), half value layer (HVL) and mean free path (MFP) for the prepared glasses have been evaluated. The MAC and Zeff values are found to increase with an increase in the BaO (for BaO-Bi2O3-B2O3 glasses) and ZnO (for ZnO-Bi2O3-B2O3 glasses) concentrations. By the addition of BaO and ZnO, a remarkable difference in HVL between the BaO and ZnO glasses is noticed. Additionally, the elastic moduli results have been measured by sound velocity at 4 MHz and computed according to Makishima-Mackenzie model and Rocherulle model. The results observed that the 30BaO-30Bi(2)O(3)-40B(2)O(3) glass system showed excellent nuclear radiation shielding and elastic properties. All the obtained results indicated that BaO-Bi2O3-B2O3 glass system has shielding properties that is better than ZnO-Bi2O3-B2O3 glass system.