Aqueous suspensions of length selected single-walled carbon nanotubes were studied by atomic force microscopy (AFM) in order to probe the influence of sonication on nanotube scission. The maximum of the tube length distribution, l(M), initially exhibits a power law dependence on the sonication time, t roughly as l(M) approximate to t(-0.5). This and the limiting behavior observed at longer times can be rationalized to first order in terms of a continuum model deriving from polymer physics. In this picture, the strain force associated with cavitation scales with the square of the nanotube length. Scission stops when the strain force falls below the critical value for nanotube disruption.