Understanding the influence of rare-earth ions in tellurite-rich glass is vital for developing the technology. With this motivation, the present study analyzes the radiation shielding, physical, structural, mechanical, and acoustic features of the tellurite glasses added Nd2O3 rare earth material. Five different glasses coded as TMNd0.0-TMNd1.9 are simulated via MCNPX Monte Carlo code by varying the concentration of neodymium oxide (Nd2O3) and the related characteristics are evaluated between 0.01 and 10 MeV. The obtained results reveal that Nd2O3 has a favorable influence on the radiation shielding characteristics of the preferred glass sample. To assess the relation between Nd2O3 concentration in tellurite glass and corresponding structural and mechanical changes in candidate glasses, Makishima-Mackenzie theory is applied and mechanical moduli are extracted. The structure and dimensionality of the preferred samples are derived based on the Bergman and Kantor model for fluid and compositions with the help of the fractal bond connectivity. In addition, the longitudinal velocity (VL$$ {V}_{\mathrm{L}} $$), transverse velocity (VS$$ {V}_{\mathrm{S}} $$), mean velocity (Vmean$$ {V}_{\mathrm{mean}} $$), and acoustic impedance (Zi$$ {Z}_{\mathrm{i}} $$) related to the TMNd glasses are evaluated.