The role of dysprosium oxide (Dy2O3)-doped PbO–B2O3–SiO2 glasses on gamma and neutron radiation shielding properties was investigated and evaluated in terms of potential use in radiation protection. The glass composition was arranged according to the formula (55–x)B2O3–25PbO–20SiO2–xDy2O3 (0 ≤ x ≤ 5) (mol%). The Monte Carlo simulation (MCNPX) code was utilised to simulate the mass attenuation coefficient (MAC) of the glasses. When photon energies were in the range of 0.015–15 MeV, the resulting simulated mass attenuation (µm) values were evaluated with conventional Phy-X/PSD database findings. The Phy-X/PSD collected data and the predicted µm findings were in good agreement. The half-value layer (HVL), effective atomic number (Zeff), exposure and energy absorption build-up factors (EBF and EABF) of the glass samples were evaluated. 5 mol% Dy2O3-doped sample has significant γ-ray shielding efficacy in the complete energy range due to lower values of HVL, higher values of MAC and effective atomic number. The build-up factors follow a similar pattern with incident photon energy and penetration depth, growing on a steeply increasing trend up to a maximum at 0.5–1.5 MeV energy, then gradually reducing as photon energy increases up to 15 MeV. The build-up factors show the same routine with penetration depth and incident photon energy. They tend to steeply rise to a peak level at 0.5–1.5 MeV energy, then gradually decrease as the photon energy increases to 15 MeV. Also, the neutron shielding ability was detected and the effective removal cross-section Σ R (cm−1) was estimated theoretically. Due to the greatest value of effective removal cross-section, 5 mol% Dy2O3-doped glass exhibits stronger neutron shielding characteristics than the other glass samples. [ABSTRACT FROM AUTHOR]