The proton-ordered ice VIII structure has been investigated by ab initio periodic Hartree-Fock calculations in the pressure interval from 0 to 30 GPa using a 6-31G** basis set, The structure was optimized by energy-minimization at different volumes, and from the resulting energy vs volume relationship; the equation of state of ice VIII was derived; The variation of the structure,intramolecular geometry, Mulliken charges, electron density, Raman spectrum, and infrared stretching vibrations with varying pressure were investigated. The agreement with existing experimental data is generally good. Nearest-neighbor hydrogen-bonded O...O distances decrease from 2.88 to 2.57 Angstrom as the pressure is increased from 0 to 30 GPa. For the same : pressure range, the intramolecular OH bond increases from 0.951 to 0.955 Angstrom (giving a dr(OH)/dP value of 0.000 14 Angstrom/GPA), the Mulliken charge on H increases from +0.386 to +0.452, the calculated bulk modulus increases from similar to 25 to similar to 160 GPa), (corresponding experimental values ire similar to 25 at 2.4 GPa and similar to 135 at 30 GPa), and the electron density redistribution is considerably enhanced. The frequency downshift of the OH stretching vibration varies from -200 cm(-1) at 2.4 GPa to -500 cm(-1) at 20 GPa; the corresponding experimental values are -300 and -650 cm(-1). Electronic density-of-states diagrams are presented.