Vibratory finishing is among the widely recognized mass finishing techniques which is used for cleaning, deburring, edge rounding, polishing, and creating an isotropic surface finish on metal parts that have undergone previous machining operations. Despite this process being straightforward and easy to implement at a very low cost and with a good degree of automation, an understanding of the basic mechanics of material removal and surface modification mechanism is lacking. In this work the potential of treating the media as a fluid is explored and a continuum mechanics based approach is taken to model the flow of media around a stationary workpiece in a computational fluid dynamics (CFD) environment. Important aspects of CFD model design and analysis are discussed and CFD derived pressure and velocity distributions are used to explain the variations in surface finishes obtained on two aluminum workpieces that were subjected to different media flow conditions. The results outlined in this thesis demonstrate the potential of using a CFD modeling approach to predict the process outcomes, while also providing a solid foundation for further modeling efforts.