Water ice is a molecular solid whose behavior under compression reveals the interplay of covalent bonding in molecules and forces acting between them. This interplay determines high-pressure phase transitions, the elastic and plastic behavior of H 2 O ice, which are the properties needed for modeling the convection and internal structure of the giant planets and moons of the solar system as well as H 2 O-rich exoplanets. We investigated experimentally and theoretically elastic properties and phase transitions of cubic H 2 O ice at room temperature and high pressures between 10 and 82 GPa. The time-domain Brillouin scattering (TDBS) technique was used to measure longitudinal sound velocities (V L) in polycrystalline ice samples compressed in a diamond anvil cell. The high spatial resolution of the TDBS technique revealed variations of V L caused by elastic anisotropy, allowing us to reliably determine the fastest and the slowest sound velocity in a single crystal of cubic H 2 O ice and thus to evaluate existing equations of state. Pressure dependencies of the single-crystal elastic moduli C ij (P) of cubic H 2 O ice to 82 GPa have been obtained which indicate its hardness and brittleness. These results were compared with ab initio calculations. It is suggested that the transition from molecular ice VII to ionic ice X occurs at much higher pressures than proposed earlier, probably above 80 GPa.