Recent observations of particle motion in vertical seismic profile surveys suggest the existence of borehole waves for which the formation horizontal particle motion is polarized in a specific azimuthal direction, possibly the direction of a local principal axis of stress. From an analysis of the static displacement of a pressurized vertical cylindrical borehole in a transversely isotropic formation with a horizontal axis of symmetry, we conclude that horizontal particle motion should not be azimuthally polarized for ''tube waves'' (lowest mode symmetric borehole wave) even in an ideal azimuthally anisotropic medium. Azimuthally polarized particle motion does exist for the ''bending mode'' of the borehole (lowest antisymmetric mode) even in isotropic formations; the polarization direction being determined by the source direction. Finite element calculations for a verticle borehole in a transversely isotropic formation with a horizontal axis of symmetry show that two bending modes with different velocities exist. The horizontal particle motion of one is polarized along the symmetry axis and the other is polarized orthogonal to that axis. At low frequencies the velocity of each approaches the velocity of a vertically propagating formation body shear wave with the same polarization direction. The recent experimental observations include one borehole arrival with a propagation velocity and a ratio of horizontal to vertical formation particle motion consistent with the hypothesis that it is a bending mode in an azimuthally anisotropic medium. The polarization direction and excitation of such a mode do not seem unreasonable. Other polarized arrivals cannot be easily explained. ¿ American Geophysical Union 1989