The volume dependence of the potential energy landscapes of glasses is examined. Glassy structures, corresponding to local potential energy minima, are compressed and expanded. The local minima often disappear with volume changes, after which the system becomes mechanically unstable and subsequently relaxes to a different, unrelated local minimum. Several characteristics of the potential energy surface are monitored as the volume is changed, including normal mode frequencies, barrier heights, and orientations and distances between the local minima and transition states. These characteristics are used Co elucidate the disappearance of the local minimum and the ensuing relaxation to a different local minimum. The disappearance of an energy minimum becomes more probable as the number of atoms in the system increases, Implications of these results are discussed with regard to pressure-induced structural rearrangements and equation-of-state properties of glasses. (C) 1997 American Institute of Physics.