Acoustic effects of vocal tract detailed structures are examined in pursuit of a realistic acoustic model of speech production. MRI-based acoustic analyses of the paranasal sinuses and the piriform fossa indicate that these cavities and branches contribute to complex patterns of natural speech spectra. Antiresonances of the paranasal sinuses are accounted for by a set of Helmholtz resonators. The total effects are statistically represented by a four-zero model. The cavities of piriform fossa cause significant changes in vowel formants as well as local antiresonances. The results suggest a more accurate vocal tract model with two side branches near the glottis.