Purpose: The purpose of this study was to explore the possible structural and material property features that may facilitate complete glottal closure in an otherwise isotropic physical vocal fold model. Method: Seven vocal fold models with different structural features were used in this study. An isotropic model was used as the baseline model, and other models were modified from the baseline model by either embedding fibers aligned along the anterior-posterior direction in the body or cover layer, adding a stiffer outer layer simulating the epithelium layer, or a combination of the 2 features. Phonation tests were performed with both aerodynamic and acoustic measurements and high-speed imaging of vocal fold vibration. Results: Compared with the isotropic one-layer model, the presence of a stiffer epithelium layer led to complete glottal closure along the anterior-posterior direction and strong excitation of high-order harmonics in the resulting acoustic spectra. Similar improvements were observed with fibers embedded in the cover layer, but to a lesser degree. The presence of fibers in the body layer did not yield noticeable improvements in glottal closure or harmonic excitation. Conclusion: This study shows that the presence of collagen and elastin fibers and the epithelium layer may play a critical role in achieving complete glottal closure.