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Vibratory conveyors are widely used to feed raw materials and small parts to processing equipment. Up to now, most of the research has focused on materials and parts that can be modeled as point masses or small blocks. This paper focuses on the conveying of cylindrical parts. In this case, the rolling motion is an essential feature of conveyor dynamics. First, the dynamic equations governing the rolling motion are stated, and the effects of friction and rolling resistance coefficients on the behavior of the system are analyzed. Then, a non-linear numerical model is developed in MATLAB. It takes into account the transition between pure rolling and rolling with sliding and the impacts of the cylindrical part on the edges of the conveyor. Numerical results showing the effect of the operative parameters of the conveyor and of friction properties on the traveled distance are presented and discussed. Finally, a comparison between numerical and experimental results is presented.