Vibratory bowl feeders are among the most versatile machines used for the feeding of small elements during the assembly process. The feeding element in a vibratory bowl feeder moves forward with sliding or hopping movement. There are two parameters that have great influence on the performance of a vibratory bowl feeder. The first parameter is the vibration angle which is the angle between the track and its vibration direction. Second parameter is the bowl feeder natural frequencies and their related mode shapes. These parameters affect the elements feeding speed and define the optimum inducing frequency in which the minimum energy would be wasted. In the first section of this MSc thesis, finite element method was utilized for vibration and modal analysis of a vibratory bowl feeder. In order to validate the model, some experiments were performed and good agreement between the simulation data and experimental data was obtained. It is shown that the vibration angle is not necessarily equal to the complementary of the spring inclination angle. The effect of some physical parameters such as spring thickness, support stiffness and bowl mass on vibration angle and the main natural frequency of the vibratory bowl feeder has also investigated. The second part of this MSc thesis focuses on the elements dynamics during the feeding process in a vibratory bowl feeder. The feeding elements in a vibratory bowl feeder are experiencing repeated impacts with friction. In order to model the behavior of the elements, a 2D numerical model based on discrete element method has been developed using C computer language. In contrast to previous researches, it is assumed that the feeding element is not a point mass and has a rectangle shape that can rotate and have three degrees of freedom. This model is capable to demonstrate both the periodic and chaotic behavior of the feeding elements. By performing the simulation for various vibration amplitudes good agreement was observed between calculated data with the experimental data reported in the literature. The effect of vibration amplitude, element shape, coefficient of friction and track angle on mean conveying velocity was evaluated and the results are presented. This model is also capable of simulating interactions between the feeding elements and it was found that the elements interactions speed up the process as the elements would climb up the track easier due to the push forces of the back elements. Although this 2D model seems to be an appropriate model for simulation of the feeding elements in a vibratory bowl feeder, it is incapable of comprising the effect of Coriolis acceleration and the contacts with the wall of the bowl. To this matter, a 3D model based on discrete element method has also been developed and the dynamic of a 3D element with six degree of freedom, which is moving on the track of the bowl has been investigated. It is shown that this 3D model is capable to demonstrate both the periodic and chaotic behavior of the feeding element, too. By performing the simulation for various vibration amplitudes, a good degree of agreement observed between calculated and experimental data reported in the literature. Using this 3D simulation, it is shown that due to the unsymmetrical forces, the element rotates as it moves forward on the track. It is also demonstrated that the Corioilis acceleration affects the radial position of the moving element. The most advantage of this 3D model is its capability in explaining the reason of existence of two maximums in the experimental graph of mean conveying velocity versus vibration amplitude. Keywords: Vibratory bowl feeder, vibration angle, finite element method, mean conveying velocity, chaos contacts, discrete element method, Coriolis acceleration.