The appropriate ground states of the Al-La and Al-Y binary alloy are calculated by using the first-principles method based on density functional theory, the solubility of La and Y elements in Al are discussed, as well as the mechanical properties of the RE precipitates. The results show that the most stable phase of Al-La and Al-Y is Al2RE compound. For three of the priority precipitates (Al3Y(R-3M), Al3Y(PM-3M) and Al11La3(IMMM)), Al3Y(R-3M) has the highest stability and strengthening capability, and the difference of the calculated solubility for La and Y in Al indicates that Y has a high solubility limit. A comprehensive elastic modulus and solubility calculations, it can be concluded that Y is the better candidate as a potential addition to enhance the Al alloy matrix.