The problem of the magnetohydrodynamical stability of bent magnetotail current sheets is considered by means of 2.5-dimensional numerical simulations. This study is focused on the cross-tail transversal mode, modeling the magnetotail flapping motions, at the background of the Kan-like magneto-plasma equilibrium. It is found that in symmetrical current sheets, both stable and unstable branches of the solution may coexist; the growth rate of the unstable mode is rather small, so that the sheet may be considered as stable at the substorm timescale. With the increasing dipole tilt angle, the sheet bends and the growth rate rises. For sufficiently large tilt angles, the stable branch of the solution disappears. Thereby, the sheet destabilization timescale shortens for an order of magnitude, down to several minutes. The analysis of the background parameters has shown that stability loss is not related to buoyancy; it is controlled by the cross-sheet distribution of the total pressure. (C) 2018 Author(s).