An anisotropic reservoir is simulated by a transversely isotropic two-phase medium, and the acoustic field excited by a multipole source in a fluid-filled borehole is investigated. The medium outside the borehole is modeled following Biot’s and homogenization theories. Similar work has only be seen in Schmitt’s [J. Acoust. Soc. Am. 86, 2397–2421 (1989)] study, but he focused his attention on the behavior of the mode waves. In this article, not only are the dispersion and excitation of the mode waves analyzed thoroughly, but the propagation mechanism of the critical refracted P and S waves corresponding to the multipole source branch cut integrations is also investigated for the first time. The effect of the vertical and horizontal permeabilities, porosity, radius, stiffnesses, and other factors on the acoustic field is analyzed.