The structural, elastic and electronic properties of ReN are investigated by first-principles calculations based on density functional theory. Two competing structures, i.e., CsCl-like and NiAs-like structures, are found and the most stable structure, NiAs-like, has a hexagonal symmetry which belongs to space group P63/mmc with a=2.7472 and c=5.8180 AA. ReN with hexagonal symmetry is a metal ultra-incompressible solid and has less elastic anisotropy. The ultra-incompressibility of ReN is attributed to its high valence electron density and strong covalence bondings. Calculations of density of states and charge density distribution, together with Mulliken atomic population analysis, show that the bondings of ReN should be a mixture of metallic, covalent, and ionic bondings. Our results indicate that ReN can be used as a potential ultra-incompressible conductor. In particular, we obtain a superconducting transition temperature T$_c$=4.8 K for ReN.
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