The local elastic structure of a single-atom Lennard-Jones glass is discussed. We show that the local pressures in this system have a large variance in their distribution, which is of the same scale as the breaking pressure. These pressures have a spatial medium range order with a characteristic length scale of 5-6 atomic distances. We find that when one decompresses the lattice the nonaffine distortions in the material depend dramatically on the lattice temperature. (C) 1999 Elsevier Science B.V. All rights reserved.