The influence of vocal fold cover layer thickness on the flow-induced vibration and voice production was studied by using a continuum-mechanics based computational model. The cover-body thickness ratio of a three-layer vocal fold was systematically varied. The effect on the vocal fold stiffness, eigenfrequencies and eigenmodes, fundamental frequencies, glottal flow rate, vocal fold vibratory dynamics, and synchronization of the eigenmodes were analyzed by using the structure eigen analysis and flowstructure interaction simulations. It was found that the cover-body layer thickness ratio significantly affected the strength and synchronization of the eigenmodes during flow-structure interactions, and ultimately affected the fundamental frequency and vibration pattern. With the increasing cover-body thickness ratio, the strength of the wave-type higher-eigenfrequency modes increased, and that resulted in a nonlinear bifurcation of the system in which the system evolved from a regular periodic vibration to a periodic doubling vibration and then back to a regular periodic vibration with increased fundamental frequencies. During the transition, the system vibrated chaotically. Because of the increased strength of the wave-type modes, the maximum divergent angle of the glottis was also increased with the increasing cover-body thickness ratio. V