In the present work, a newly produced PbO-BaO-B2O3 glass system’s mechanical, physical, and radiation absorption capabilities were studied to determine the effectivity of B2O3 substitution by ZnO. The melt-quench process produced the glasses utilized in the present investigation. The melting point used was 1000 °C, and the temperature at which they were annealed was 400 °C. The experimental measurement of the density for manufactured glass samples was conducted using Archimedes’ theory. It was observed that all density values of the fabricated glasses were raised when the concentration of ZnO was increased from 0 to 20 mol.%. Based on the model proposed by Makishima and Mackenzie from Young, bulk, shear, and longitudinal moduli, it was observed that there was a decrease as the concentration of ZnO was increased in the manufactured glasses. Microhardness was found to be reduced from 4.692 GPa to 4.218 GPa, while the Poisson ratio was found to be decreased from 0.234 to 0.229 when the percentage of ZnO was raised from 0 to 20 mol.%. In contrast, the assessment of radiation shielding qualities through the utilization of Monte Carlo software simulation demonstrates an augmentation in the radiation absorption capability of the manufactured glass samples due to the exchange between B2O3 and ZnO compounds. We used the MCNP5 code to study the radiation shielding properties in a wide energy range of 0.03–2.605 MeV. The linear attenuation coefficient LAC of the produced glass samples increased from 0.315 cm−1 to 0.369 cm−1 when the ZnO concentrations were enriched from 0 to 20 mol.%, respectively.