The radiation shielding properties of xPbO-(100-x)TeO2, x = 10, 20, and 30 mol% binary glasses and y[ZnO]-(100-y)[70(TeO2)-30(PbO)] y = 15, 20, and 25 mol% ternary glasses were investigated using Geant4 simulations and the newly developed Phy-X/PSD program. The glasses' gamma shielding abilities were assessed using their mass attenuation coefficient (mu/p), mean free path (MFP), effective atomic number (Z(eff)), and half value layer (HVL) values. The neutron shielding ability was evaluated by determining the removal cross-section (RCS) values, which were 0.097, 0.101, and 0.103 cm(-1) for binary PbO-TeO2 (PT) glasses and 0.118, 0.116, and 0.114 cm(-1) for ternary ZnO-PbO-TeO2 (PTZ) glasses. The gamma and neutron shielding features of the glasses were compared with those of various ordinary concretes and Pb-free, Pb-based, and commercial glasses. The addition of PbO changed the gamma and neutron properties of the PT glasses, while the addition of ZnO demonstrated a different trend in the gamma properties of the PTZ glass system.