By molecular-dynamics simulation, we investigate the possible existence of a crumpling transition for a model of tethered membranes, where the particles are tethered by a continuous potential. For distant-neighbor interactions, the potential is repulsive and contains a variable hard-core diameter parameter. By varying this parameter, we are able to study in detail the effect of self-avoidance. Our results suggest the interpretation that self-avoiding two-dimensional tethered membranes are asymptotically flat, even without an explicit bending rigidity, and that there is no crumpling transition except for phantom membranes. © 1989 The American Physical Society.