Understanding the influence of Rare-Earth Elements (REEs) in tellurite-rich glass is vital for developing the technology due to applications of REEs in various technologies like television displays, solid-state lasers, tunable waveguides, tunable fiber grating, etc. With this motivation, the present work analyzes the radiation shielding, physical, structural, mechanical and acoustic properties of the (1-x)TeO2-xLa(2)O(3): x = 5, 7, 10, 15 and 20 (mol%) glass samples. For this purpose, using user-friendly MCNPX Monte Carlo code the LaTe1-LaTe5 glass samples are irradiated, and thus the radiation shielding competencies are obtained for wide energy spans ranging from 0 to 15 MeV. The derived Half Value Layer (Delta(0.5)) outcomes are compared with the theoretical studies namely, Phy-X:PSD results for some selected energies. In addition, the mechanical features are obtained by the (Makishima Mackenzie) Mak-Mac Model. Based on the mechanical characteristics, acoustic properties are extracted and reported in this paper. 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 (FBC). Findings show that La2O3 is an effective Rare Earth (RE) material to increase the shielding ability of the LaTe glass samples from LaTe1 to LaTe5. Furthermore, from the obtained results can be concluded that the La2O3 RE material is able to break the glass structure and increase the linkage, and thus, the acoustic properties will be improved.