Elastic collisions in the transplanckian region, where the center-of-mass energy is much larger than the fundamental gravity mass scale, can be described by linearized general relativity and known quantum-mechanical effects as long as the momentum transfer of the process is sufficiently small. For larger momentum transfer, non-linear gravitational effects become important and, although a computation is lacking, black-hole formation is expected to dominate the dynamics. We discuss how elastic transplanckian collisions can be used at high-energy colliders to study, in a quantitative and model-independent way, theories in which gravity propagates in flat extra dimensions. At LHC energies, however, incalculable quantum-gravity contributions may significantly affect the experimental signal. (C) 2002 Published by Elsevier Science B.V.