The current study examines the physical, structural, mechanical, and radiation shielding properties of a series of (75-x) TeO2 -15 MgO -10Na2O -x Nd2O3: 0.0 <x < 2.0 mol% glasses. Nine distinct glasses coded as Nd-0.0 to Nd-2.0 are simulated via MCNPX Monte Carlo code by the varying composition of Nd2O3 (Neodymium oxide) and the related characteristics are evaluated between 0.015 and 10 MeV. The Beer-Lambert Law and Makishima–Mackenize theory are used to assess the preferred glass samples' radiation shielding and mechanical characteristics. Acquired results show that the Nd-2.0 glass sample gives the best gamma photon shielding performance. In addition, the computed physical features reveal that increasing the Nd2O3 contents from Nd-0.0 to Nd-2.0 leads to a tightly packed glass structure. Finally, it can be concluded that the candidate glass samples can be used as shielding substances against gamma photons and are able to enhance the structural and mechanical qualities.