Structural, elastic and electronic properties of ReO2 are investigated by first-principles calculations based on density functional theory. The ground state of ReO2 has an orthorhombic symmetry which belongs to space group Pbcn with α = 4.7868 Å b = 5.5736 Å and c = 4.5322 Å. The calculated bulk moduli are 322 GPa, 353 GPa, and 345 GPa for orthorhombic, tetragonal, and monoclinic ReO2, respectively, indicating that ReO2 has a strong incompressibility. ReO2 is a metal ductile solid and presents large elastic anisotropy. The obtained Debye temperatures are 850K for orthorhombic, 785K for tetragonal, and 791K for monoclinic ReO2.