Computational models of the flow-induced vibrations of the vocal folds are powerful tools that can be used in conjunction with physical experiments to better understand voice production. This thesis research has been performed to contribute to the understanding of vocal fold dynamics as well as several aspects of computational modeling of the vocal folds. In particular, the effects of supraglottal geometry have been analyzed using a computational model of the vocal folds and laryngeal airway. In addition, three important computational modeling parameters (contact line location, Poisson's ratio, and symmetry assumptions) have been systematically varied to determine their influence on model output. Variations in model response were quantified by comparing glottal width, frequency, flow rate, open quotient, pressures, and wave velocity measures. In addition, the glottal jet was qualitatively analyzed. It was found that for various supraglottal geometries (either symmetrically or asymmetrically positioned), there was little asymmetry of the vocal fold motion despite significant asymmetry in the glottal jet. In addition, the vocal fold motion was most symmetric when consistent jet deflection was present (even if asymmetric). Inconsistent deflection of the glottal jet led to slightly larger asymmetries in vocal fold motion. The contact line location was found to have minimal impact on glottal width, frequency, and flow rate. The largest influence of the contact line location was seen in predicted velocity fields during the closed phase and in the pressure profiles along the vocal fold surfaces. Variations in Poisson's ratio strongly affected vocal fold motion, with lower Poisson's ratios resulting in larger amplitudes. The model did not vibrate when a Poisson's ratio of 0.49999 was used. The response of a full model (with two vocal folds) was shown to vary slightly from that of a half model (one vocal fold and a symmetry boundary condition), the greatest difference being in the deflection and dissipation of the glottal jet. It was concluded that for many scenarios the half model will be sufficient for modeling vocal fold motion; however, a full model is suggested for studies of material asymmetry or glottal jet dynamics. Application of these results to computational models of the vocal folds will lead to improved modeling and understanding of vocal fold dynamics.