Three zinc barium-borate glasses were produced in the current work, incorporating different metal oxides (MO) (CaO, TiO2, and CuO) via the melt quenching technique under a 1100 °C melting temperature for 60 min. The fabricated samples' density is 4.112 g/cm3, 4.157 g/cm3, and 4.261 g/cm3 for glasses dopped with CaO, TiO2, and CuO, respectively. Additionally, the Makishima-Mackenzie model was employed to evaluate the effect of metal oxides on the fabricated glasses' mechanical properties. The study shows that the glasses with TiO2 have the highest mechanical moduli and microhardness which reach 4.67 GPa. The gamma-ray shielding properties in the 0.033–2.506 MeV energy interval were estimated by applying Monte Carlo simulation. The study demonstrates that the glass samples containing CuO exhibit the highest linear attenuation coefficient (LAC) when compared to the glasses containing Ca and TiO2 compounds. The LAC of the CuO-doped glasses varied between 28.367 cm−1 and 0.163 cm−1 when the photon energy was raised between 0.033 MeV and 2.506 MeV. Also, the study shows good shielding parameters (half-value layer, lead's equivalent thickness, and radiation protection efficiency) for the glasses doped CuO compared to glasses doped Ca and TiO2.