We study the behavior of a naturally straight highly extensible elastic filament subjected to large
extensional and twisting strains. We find that two different phases can coexist for a range of parameter
values: the plectoneme and the solenoid. A simple theory based on a neo-Hookean model for the material
of the filament and accounting for the slender geometry suffices to explain these observations, and leads to
a phase diagram that is consistent with observations. Extension and relaxation experiments on these
phases show the presence of large hysteresis loops and sawtoothlike force-displacement curves which are
different for the plectoneme and the solenoid.