  We study dynamical consequences of the kink instability of a twisted coronal
flux rope, using the force-free coronal loop model by Titov & D\'emoulin (1999)
as the initial condition in ideal-MHD simulations. When a critical value of the
twist is exceeded, the long-wavelength ($m=1$) kink mode develops. Analogous to
the well-known cylindrical approximation, a helical current sheet is then
formed at the interface with the surrounding medium. In contrast to the
cylindrical case, upward-kinking loops form a second, vertical current sheet
below the loop apex at the position of the hyperbolic flux tube (generalized X
line) in the model. The current density is steepened in both sheets and
eventually exceeds the current density in the loop (although the kink
perturbation starts to saturate in our simulations without leading to a global
eruption). The projection of the field lines that pass through the vertical
current sheet shows an S shape whose sense agrees with the typical sense of
transient sigmoidal (forward or reverse S-shaped) structures that brighten in
soft X rays prior to coronal eruptions. The upward-kinked loop has the opposite
S shape, leading to the conclusion that such sigmoids do not generally show the
erupting loops themselves but indicate the formation of the vertical current
sheet below them that is the central element of the standard flare model.
