Structural relaxations, electronic properties, and surface energies of ReB2 (001) and (110) surfaces with various terminations are investigated with a first-principles method. It is found that the surface interatomic spacings of ReB2 (001) and (110) surfaces are different from those of the bulk structure. The vertical spacings between the first and second layers of the studied surfaces are contracted. The (001)-Re surface is likely to be stable without introducing a large relaxation. Among these surfaces, only the (110) surface has surface rumpling, and the Re atoms on its first layer are apt to move inward. After atomic relaxation, some covalent bonds formed by the outmost atoms of the relaxed surfaces are shorter than those of the bulk system, which indicates that the covalent B-B and Re-B bonds of the surface layer have been strengthened. An analysis of surface energies shows that after relaxation, the (001)-Re surface is more stable than other types of surfaces. (c) 2012 Elsevier B.V. All rights reserved.