The present study is dedicated to deriving radiation shielding and mechanical features of the tellurium dioxide-zinc oxide-nickel oxide (TeO2–ZnO–NiO) preferred glass systems. The radiation shielding and mechanical parameters have been obtained by leveraging the FLUKA Monte Carlo (MC) approach and theoretical analysis. Attenuation factors have been carried out for different ratios of Te: Zn (i.e., 4:1, 7:3, 3:2) and 2 cm thickness glass specimen. Three NiO mole fractions are investigated for this purpose. Among the three-glass series, 7:3 specimens possess the highest radiation shielding, improving the space-efficiency. In addition, the Zeff increases with the rising TeO2 concentration in the glass structure, especially in the high energy range. Furthermore, reducing the amount of ZnO as a network modifier in the glass increases the molar volume. Moreover, we successfully increased the mechanical module of the provided glass specimens utilizing MM model. The outcomes of the present work are suitable for further studies related to the ternary Te glass series.