The elastic response and critical strain of single-walled carbon nanotubes (SWT's) are investigated by means of quenched molecular dynamics simulations using the Tersoff-Brenner potential. The results of this discrete model are found to be in agreement with calculations based on continuum elasticity theory for tube radii greater than 10.0 Angstrom. However, for tube radii less than 10.0 Angstrom the two models diverge. It is shown that there is a correlation between the critical strain and the experimentally measured abundance of SWT's with various radii. Based on this information, we suggest a model to explain the role of structural stability in determining the radial distribution of SWT's.