  First results from a high-resolution three-dimensional nonlinear numerical
study of the kink oscillation are presented. We show in detail the development
of a shear instability in an untwisted line-tied magnetic flux tube. The
instability produces significant deformations of the tube boundary. An extended
transition layer may naturally evolve as a result of the shear instability at a
sharp transition between the flux tube and the external medium. We also discuss
the possible effects of the instability on the process of resonant absorption
when an inhomogeneous layer is included in the model. One of the implications
of these results is that the azimuthal component of the magnetic field of a
stable flux tube in the solar corona, needed to prevent the shear instability,
is probably constrained to be in a very specific range.
