Many earth formations are characterized as transversely isotropic (TI) media. In acoustic logging through a vertical borehole, the S-wave TI property has traditionally been determined from borehole monopole Stoneley-wave measurements, but the feasibility of shear-TI estimation from dipole flexural waves has not been fully investigated. We have developed a methodology to determine the TI parameters from borehole dipole-flexural wave data. Our analysis shows that the Stoneley wave is sensitive to the TI property mainly in an acoustically slow formation, and the sensitivity diminishes when the formation becomes faster. The advantage of the flexural wave over the Stoneley wave is that the former wave is sensitive to the TI property in the slow and fast formations, provided the wave measurement is made in a broad frequency range in which the flexural-wave dispersion characteristics from low to high frequencies can be used. By calculating the theoretical flexural-wave dispersion curve for the TI formation and using it to fit the measured wave dispersion data, we can simultaneously determine the vertical and horizontal S-wave velocities, from which the S-wave TI parameter is obtained. Application of our methodology to field data processing shows that the TI parameter estimated from the flexural wave is almost identical to that from the Stoneley wave for a slow formation. For a fast formation, the flexural-wave result is more accurate and reliable compared with the Stoneley-wave result. Our study, thus, introduces a novel application of dipole acoustic logging.