Sound wave propagation in a vocal tract model is investigated using a three-dimensional finite-element method (FEM). In the present study, a new FEM model is proposed with branches of the vocal tract measured by MRI. The branches correspond to the pyriform fossa and the vallecula of epiglottis. Using this vocal tract model, sound pressure and particle velocity are computed. Evaluations are as follows: first, the difference of vocal tract transfer function (VTTF) between the model with the branches and without; and, second, the difference of VTTF between the model taking into account the wall impedance of the tongue and not taking it into account. From the simulation results, it is shown that formant peak levels are influenced by the branches in the high-frequency region over 4 kHz, and the distribution of the sound-pressure pattern around the branches is seen by a complicated spherical surface. Furthermore, in the case of the model with the wall impedance, it is shown that the formant peak levels have a tendency to decline, due to the loss on the wall.