The Mg-Zn and Al-Zn binary alloys have been investigated theoretically under static isotropic pressure. The stable phases of these binaries on both initially hexagonal-close-packed (HCP) and face-centered-cubic (FCC) lattices have been determined by utilizing an iterative approach that uses a configurational cluster expansion method, Monte Carlo search algorithm, and density functional theory (DFT) calculations. Based on 64-atom models, it is shown that the most stable phases of the Mg-Zn binary alloy under ambient condition are MgZn 3 , Mg 19 Zn 45 , MgZn, and Mg 34 Zn 30 for the HCP, and MgZn 3 and MgZn for the FCC lattice, whereas the Al-Zn binary is energetically unfavorable throughout the entire composition range for both the HCP and FCC lattices under all conditions. By applying an isotropic pressure in the HCP lattice, Mg 19 Zn 45 turns into an unstable phase at P≈10 GPa, a new stable phase Mg 3 Zn appears at P 20 GPa, and Mg 34 Zn 30 becomes unstable for P 30 GPa. For FCC lattice, the Mg 3 Zn phase weakly touches the convex hull at P 20 GPa while the other stable phases remain intact up to ≈120 GPa. Furthermore, making use of the obtained DFT results, bulk modulus has been computed for several compositions up to pressure values of the order of ≈120 GPa. The findings suggest that one can switch between Mg-rich and Zn-rich early-stage clusters simply by applying external pressure. Zn-rich alloys and precipitates are more favorable in terms of stiffness and stability against external deformation.