The baiji (Lipotes vexillifer) of the Yangtze River possesses a sophisticated biosonar system. In this study, a finite element approach was used to numerically investigate the propagation of acoustic waves through the head of the Yangtze River dolphin, which possesses an inhomogeneous and complex structure. The acoustic intensity distribution predicted from models with and without the melon and/or skull showed that the emitted sound beam was narrow and formed a highly directed acoustic beam, and the skull and melon significantly enhanced the directional characteristics of the emitted sound. Finally, for a short duration impulsive source, the emitted sound pressure distributions were also simulated at different propagation times. The results provide useful information for better understanding the operation of the biosonar system in this rare and perhaps extinct animal.