In this paper, the mechanical properties, electronic structures, and thermodynamic properties of Ag2Ga and CuGa2 under pressure are studied using the first‐principles method based on Density functional theory (DFT). With the increase in pressure, the equilibrium lattice constants (a/a0 and c/c0) and volume ratio (V/V0) of Ag2Ga and CuGa2 continuously decrease. The elastic constants show that Ag2Ga and CuGa2 are mechanically stable under pressures of 0–20 GPa, and the increase in pressure improves their deformation resistance. The results of Young's modulus (E) show that the hardness of CuGa2 is higher than that of Ag2Ga. The results of Cauchy pressure (C12 ‐ C44) and B/G ratio show that the plasticity of Ag2Ga and CuGa2 can be maintained with the increase in pressure. By analyzing the density of states (DOS), charge density difference (CDD), and population, the influence of pressure on electronic structure is studied. The calculated Debye temperature (θD) shows that the covalent bond of CuGa2 is stronger.