Quenched molecular dynamics simulations are used to investigate the elastic behavior of open-ended, free-standing, single wall, carbon nanotubes. Interatomic interactions are described by a Tersoff-Brenner potential. The tubes' response to axial compression is examined and typical failure modes as well as stress-strain curves for a number of tube radii are shown. Data collected are used to calculate Young's modulus for the tubes and to develop a simple formula that approximates this quantity over a wide range of tube radii. (C)1997 Published by Elsevier Science Ltd.