The glasses had the compositions 5Al₂O₃-29Na₂O-(66−x)B₂O₃-xBi₂O₃ with (0 ≤ x ≤ 20 mol%) are prepared by melt quenching technique for serving as competitive candidates for radiation shielding. The radiation shielding and mechanical properties of the prepared glasses are presented and discussed in details. The mass attenuation coefficient (μ/ρ) which is the basic parameter in order to evaluate the interaction of radiation with shielding materials were calculated in MCNPX (version 2.6.0) code, and the results were compared with those obtained by XCOM and XMuDat programs. The simulation results match most of the XCOM and XMuDat data very well. Additionally, the results revealed that both (μ/ρ) and the effective atomic number (Z_eff) of the prepared glasses increase with increasing Bi₂O₃ from 0 to 20 mol. %. It is found that the removal cross-sections, Σ_R values for the prepared glasses lie within the range 0.0932 – 0.1425 cm⁻¹.