Tube-wave characteristics, namely velocity and polarization, are affected by borehole anomalies related to nonhydrostatic tectonic stress. The anomalies we consider are borehole ellipticity, azimuthal anisotropy as modeled by a rotated transversely isotropic medium, and borehole breakouts as modeled by local heterogeneities in elastic properties. The low-frequency tube-wave velocity is obtained by a variational approach to a plane-strain, static-equilbrium problem. We solve the problem with hole ellipticity analytically and the problem with azimuthal anisotropy numerically by a finite-element method. The results show that weak ellipticity has a negligible effect on the tube-wave velocity: a relative variation of 10 percent in the main diameters of the hole produces a perturbation of only 0.5 percent in the velocity. However, localized damage to the hole can reduce tube-wave velocity significantly. Furthermore, for tube-wave polarization, it is unrealistic to obtain deviations from the radial direction greater than 15 degrees, which makes it difficult to obtain any valuable information on the stress directions from the tube wave.