A stability analysis of the antisymmetric ballooning mode is presented for the tail-like magnetic models within ideal MHD. The analysis particularly emphasizes the potential importance of the field-aligned variation of the local field curvature. First, it is found that the tail field models of Kan [1973> are stable against the antisymmetric ballooning mode because of the strong stabilizing effect of the field line bending. In such models, the field curvature is significant only in the narrowly limited region, namely, very near the equatorial plane from which it then rapidly declines, more rapidly than 1/B, along the field line. Then, the antisymmetric ballooning mode is studied in a magnetic field model in which the field curvature is assumed to vary as 1/B over some small portion from the equatorial point along the field line. For such a model, two criteria for the instability are proposed, one as a necessary condition and the other as a sufficient condition. Not only a sufficient pressure gradient and/or a high-plasma beta, but also a sufficient field-aligned portion of a substantial curvature, seem necessary for a tail-like field line to become unstable to the antisymmetric ballooning mode. As a specific example, it is shown that a high-beta, tail field line can suffer from an antisymmetric ballooning instability if the field line has a geometrical roundness over a distance of Rce, the equatorial radius of the field curvature, from the equatorial position. ¿ American Geophysical Union 1996