[en] By means of the two-fluid model, the kink stability of a long thin field-reversed ion layer immersed in a dense low-temperature background plasma is studied theoretically. The two-fluid variational quadratic form with the assumption of rigid displacements in the radial direction yields a new kink stability condition that includes the effect of the non-zero real frequency of the modes, which is due to the inertia of the ion layer. This effect is essential to explain the numerical results of Harned. As the ratio of the density of the background plasma to that of the ion layer increases, this new kink stability condition reduces to the conventional condition. The physical mechanism for the kink instability is discussed by the analogy with the electrostatic two-stream instability. (author)