Ab initio calculations incorporating the effects of electron correlation are reported for the quadrupole and hexadecapole moments, and the static dipole polarizability of I2. The calculations are based on finite-field, fourth-order, many-body perturbation theory. Coupled self-consistent-field calculations of the dependence of these properties on the bond length, and of some higher static polarizabilities are also reported. A small discrepancy is found between our calculated dipole polarizability anisotropy and a value measured by laser assisted molecular beam spectroscopy.