We present elastic moduli, gamma radiation attenuation characteristics, and transmission factor of barium–tungstate–phosphate (BTP) glasses with the chemical formula (60-y)BaO-yWO3-40P2O5, where y = 10 (S1)–40 (S4) in steps of 10 mole%. Different types of mathematical and simulation approaches, such as the Makishima-Mackenzie model, the Monte Carlo method, and the online Phy-X/PSD software, are utilized in terms of determining these parameters. The total packing density (Vt) is enriched from 0.607 to 0.627, while the total energy dissociation (Gt) is enriched by increasing the WO3 content (from 52.2 (kJ/cm3). In the investigated glasses, increasing tungstate trioxide (WO3) contribution enhanced Young’s, shear, bulk, and longitudinal moduli. Moreover, Poisson’s ratio is improved by increasing the WO3 content in the BTP glasses. The 20BaO-40WO3-40P2O5 sample possessed the highest values of both linear (µ) and mass attenuation (µm) coefficients, i.e., (µ, µm)S4 > (µ, µm)S3 > (µ, µm)S2 > (µ, µm)S1. Moreover, the 20BaO-40WO3-40P2O5 sample had the lowest values of half (HVL) and tenth (TVL) layers, i.e., (half, tenth)S4 < (half, tenth)S3 < (half, tenth)S2 < (half, tenth)S1. The effective atomic number (Zeff) of the studied glasses has the same behavior as µ and µm. Finally, the 20BaO-40WO3-40P2O5 is reported with the minimum values of transmission factor (TF) for all the BTP investigated at a thickness of 3 cm. In conclusion, the sample with composition 20BaO-40WO3-40P2O5 which has the maximum WO3 reinforcement may be a beneficial glass sample, along with its advanced mechanical and gamma ray shielding properties.