The structural stability and elastic and electronic properties of rhenium borides with different boron concentration are calculated systemically by means of first principle total energy calculations. The total energy calculations reveal that the WC-type structure is more energetically favorable for ReB and that the Re2P-type structure is more preferred for Re2B. The formation enthalpy of these borides have been studied by the solid synthesis routes. The calculated elastic properties indicate that Re2B3, ReB, and Re2B phases are also potential hard materials. Although valence-electron density was often employed to evaluate elastic properties of materials, our calculations indicate that the bulk elastic properties of these borides are not direct correlation with their valence-electron density. The analysis of electronic structure, charge density distribution, and Mulliken overlap population provides further understanding of the elastic and superconductivity properties of these borides.