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Understanding and predicting the compositional dependence of the stiffness of silicate glasses is key for various technological applications. Here, we propose a new topological model for predicting the Young's modulus of silicate glasses. We show that the Young's modulus is governed by the volumetric density of bond-stretching and bond-bending topological constraints acting in the atomic network. The predicted Young's modulus values offer an excellent agreement with molecular dynamics and experimental data over a wide domain of compositions (the entire calcium aluminosilicate ternary system) and a large range of Young's modulus values (from around 80 to 160 GPa).