The polarizability and quadrupole moment of a hydrogen molecule enclosed within an infinite-walled spheroidal box are calculated as functions of the hox size, for a range corresponding to nominal pressures up to lo5 kbar. A five-term James and Coolidge variational wave function is employed and the Kirkwood approximation is used for the polarizability. Comparison is made with similar calculations for the H2+ molecule-ion and the II atom, and also with recent density-functional calculations. The box model proves to greatly exaggerate the compression of the H2 bond with pressure but nonetheless yields a realistic correlation of vibrational frequency with internuclear distance. Renormalizing the pressure scale for the box model using results of the densityfunctional calculation is found to decrease markedly the predicted variation with pressure for several properties, including the polarizability, quadrupole moment, bond length, vibrational frequency, and electronic kinetic energy. When combined with the Herzfeld criterion the predicted volume dependence of the polarizability fails to give a transition to the metallic phase.