The stability, mechanical property, electronic structure, and Debye temperature of Al‐Cu‐X ternary compounds formed by X (Co, In, Ni, Pd, Ge, Ca) doped AlCu are systematically studied by first‐principles calculations based on density functional theory (DFT). The cohesive energy and formation enthalpy results of Al‐Cu‐X show that the structure is thermodynamically stable, which are consistent with the data previously reported. Elastic modulus results that are estimated by Voigt‐Reuss‐Hill approximation. It shows that Co, Ni, and Pd increase the bulk modulus of AlCu, while In, Ge, and Ca decrease the bulk modulus of AlCu. Co, In, Ni, Pd, Ge, and Ca decrease the shear modulus and Young's modulus of AlCu. In addition, the anisotropy of Al‐Cu‐X is studied by different anisotropy indexes and Young's modulus spatial distribution figure. The electronic structures of Al‐Cu‐X ternary compounds are calculated and analyzed. It shows that the Co, In, Ni, and Pd elements are mainly hybridized with the Cu‐d orbital, while Ge and Ca are hybridized with the Al‐p orbital. Moreover, the sound velocity and Debye temperature of Al‐Cu‐X are discussed.