This manuscript presents a theoretical analysis of the elastic properties of ZnO−Na2O−Al2O3−B2O3 (in molar %) glass. The elastic moduli were calculated in terms of Makishima–Mackenzie theory and bond compression model. Addition effect of ZnO on the elastic moduli was investigated according to bond compression model in terms of the number of network bonds, the mean cross-link density, average stretching force constant, atomic ring size, and the ratio Kbc/Ke of the glass systems. Young's modulus, packing density and Poisson's ratio have been calculated and analyzed according to Makishima–Mackenzie model. The results indicate that the elastic moduli and the dimensionality of these glasses are sensitive to the increase in the zinc oxide content.