Carbon nanotubes are expected to have incredible mechanical properties. Before they can be used intelligently in engineering applications, the capabilities and limitations of these properties must be well understood. This research measured the strain-to-failure of single-wall carbon nanotubes (SWNTs) by elastically straining suspended SWNT ropes using an atomic force microscope in lateral force mode. The ropes experienced multiple scanning cycles at high strains with no plastic deformation. The nanotube ropes were observed to strain as elastic strings, instead of as stiff beams. A maximum strain of 5.9 +/- 0.9% was observed, which led to a lower bound on the yield strength of 45 +/- 7 GPa for single-wall carbon nanotubes. These results are the first experimental evidence that supports the theoretical strain-to-failure of 5% for SWNTs. This research helps to establish single-wall nanotubes as a structural material by further quantifying their mechanical properties.