A series of borotellurite glass system doped with copper oxide was synthesized using the method of melt quenching. The density of the glass decreases whereas its molar volume increases in respect to copper oxide concentration. The amorphous nature of prepared glasses was proven with the utilisation of XRD spectra. Meanwhile, the glass samples’ elastic properties are determined from the measurement of longitudinal and shear velocities using ultrasonic technique. The longitudinal modulus, shear modulus, bulk modulus and Young’s modulus will show an irregular trend that fluctuates. FLUKA Monte Carlo code is implemented to determine the shielding features at gamma energy 0.3565, 0.6616, 0.8348 and 1.3325 MeV. Linear attenuation coefficients acquired from FLUKA and XCOM are found to be in good agreement with relative difference < 1%. The glass sample B2O3TeO2CuO1 (with highest percentage of TeO2) is found to be the best shielding glass material in this study.