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This study investigates the elastic properties and the photon and neutron shielding properties of TeO2–MgO–Na2O–Nd2O3 glasses, as well as the mass stopping power and projected range of alpha and proton charged particles using SRIM software. PHITS 3.22, MCNP6.2 N-particle Monte Carlo codes and XCOM software were utilised to compute the mass attenuation coefficient (μ / ρ). The simulated and theoretical results were found to be very similar. The increase in μ / ρ values was caused by the addition of neodymium to the glasses. The lowest mean free path, half-value layer and tenth-value layer values were observed at the highest Nd2O3-doped sample. This showed that adding neodymium to glasses improves their photon radiation reduction ability. The glasses' fast neutron removal cross-sections (ΣR) were computed and the effective atomic number (Zeff) and effective electron density (Neff) were calculated using Phy-X / PSD software. The results revealed that the 75TeO2–15MgO–10Na2O glass is capable of stopping (proton and alpha) charged particles. In terms of photon and neutron attenuations, the glass system is recommended as a shielding material. In addition, the elastic properties of the samples were determined using bond compression and Makishima and Mackenzie method. According to both models, as the additive ratio increased, an improvement was observed in the elastic properties. [ABSTRACT FROM AUTHOR]