The vocal folds are an essential component of human speech production and communication. Advancements in voice research allow for improved voice disorder treatments. Since in vivo analysis of vocal fold function is limited, models have been developed to simulate vocal fold motion. In this research, synthetic and computational vocal fold models were used to investigate various aspects of vocal fold vibratory characteristics. A series of tests were performed to quantify the effect of varying material and geometric parameters on the models' flow-induced responses. First, the influence of asymmetric vocal fold stiffness on voice production was evaluated using life-sized, self-oscillating vocal fold models with idealized vocal fold geometry. Asymmetry significantly influenced glottal jet flow, glottal area, and vibration frequency. Second, flow-induced responses of simplified and MRI-based synthetic models were compared. The MRI-based models showed remarkable improvements, including less vertical motion, alternating convergent-divergent glottal profile patterns, and mucosal wave-like movement. Third, a simplified model was parametrically investigated via computational modeling techniques to determine which geometric features influenced model motion. This parametric study led to identification and ranking of key geometric parameters based on their effects on various measures of vocal fold motion (e.g., mucosal wavelike movement). Incorporation of the results of these studies into the definition of future models could lead to models with more life-like motion.