  The force-free coronal loop model by Titov & D\'emoulin (1999} is found to be
unstable with respect to the ideal kink mode, which suggests this instability
as a mechanism for the initiation of flares. The long-wavelength ($m=1$) mode
grows for average twists $\Phi\ga3.5\pi$ (at a loop aspect ratio of $\approx$
5). The threshold of instability increases with increasing major loop radius,
primarily because the aspect ratio then also increases. Numerically obtained
equilibria at subcritical twist are very close to the approximate analytical
equilibrium; they do not show indications of sigmoidal shape. The growth of
kink perturbations is eventually slowed down by the surrounding potential
field, which varies only slowly with radius in the model. With this field a
global eruption is not obtained in the ideal MHD limit. Kink perturbations with
a rising loop apex lead to the formation of a vertical current sheet below the
apex, which does not occur in the cylindrical approximation.
