Al–Mg–Si alloys are used in aircraft, train, and car manufacturing industries due to their advantages, which include non-corrosivity, low density, relatively low cost, high thermal and electrical conductivity, formability, and weldability. This study investigates the bulk mechanical properties of Al–Mg–Si alloys and the influence of the Si/Mg ratio on these properties. The Al cell was used as the starting structure, and then nine structures were modeled with varying percentages of aluminium, magnesium, and silicon. Elastic constant calculations were conducted using the stress–strain method as implemented in the quantum espresso code. This study found that the optimum properties obtained were a density of 2.762 g/cm³, a bulk modulus of 83.3 GPa, a shear modulus of 34.4 GPa, a Vickers hardness of 2.79 GPa, a Poisson’s ratio of 0.413, a Pugh’s ratio of 5.42, and a yield strength of 8.38 GPa. The optimum Si/Mg ratio was found to be 4.5 for most of the mechanical properties. The study successfully established that the Si/Mg ratio is a critical factor when dealing with the mechanical properties of the Al–Mg–Si alloys. The alloys with the optimum Si/Mg ratio can be used for industrial applications such as plane skins and mining equipment where these properties are required.