  We consider the elastic deformation of a circular cylindrical sector composed
of an incompressible isotropic soft solid when it is straightened into a
rectangular block. In this process, the circumferential line elements on the
original inner face of the sector are stretched while those on the original
outer face are contracted. We investigate the geometrical and physical
conditions under which the latter line elements can be contracted to the point
where a localized incremental instability develops. We provide a robust
algorithm to solve the corresponding two-point boundary value problem, which is
stiff numerically. We illustrate the results with full incremental displacement
fields in the case of Mooney-Rivlin materials and also perform an asymptotic
analysis for thin sectors
