The poloidal mode is most often observed at the outer edge of the ring current during storm time enhancements. It is usually thought to be driven by the gradient in the hot particle pressure. Besides large azimuthal mode number m (~100), these waves have periods of ≳100 s (Pc 4 and 5), dominant magnetic fluctuations in the radial (hence the name poloidal) or parallel direction, and second-harmonic structure (single node at equator) for the azimuthal component of the electric field or the radial velocity component. One crucial question is what determines the radial extent of the mode. Ideal MHD predicts that the mode structure will be singular about the toroidal mode (azimuthal fluctuations in velocity and magnetic field) resonant surface. One theory that seeks to explain the radial structure of the poloidal mode (still within the framework of ideal MHD) is that of Vetoulis and Chen [1994, 1996>. They proposed that a finite width poloidal mode might exist in a region where there is a dip in the square of the second-harmonic poloidal frequency fpol-2. The energy may leak out of the region of localization to be absorbed at a toroidal resonance, but if the dip in fpol-22 is large enough with the mode frequency down toward the minimum, the rate of leakage may be slow. In this paper, we examine their theory using two-dimensional linear MHD simulations in dipole geometry. We find that the theory is mathematically correct; the poloidal mode can be localized in a region of depressed fpol-2. In order for this to happen, a special kind of pressure profile is required, one having a large second derivative with respect to L shell. Satellite data should be used to examine whether or not such pressure profiles occur during the time of observed high-m poloidal modes. ¿ 1998 American Geophysical Union