Eigen-frequencies and shapes of the non-local magnetic kink-modes m=1, n>1 in a field reversal pinch are obtained in cylindrical force-free approximation by shooting method. The mode profile and the resistive layer containing the resonant surface of the internal kinks are calculated numerically. Instability is revealed, both for external and internal modes, which is not effected by resistive layer in plasmas with high conductivity, it is determined by the current gradient due to the high paramagnetic parameter in the pinch core.