Although vibratory finishing machines have been widely employed in industry for over 50 years, modeling the vibratory excitation system of the machine has not been previously published. This paper proposes a novel mathematical model of the bowl type vibratory finishing machine. This model is used to analyze the dynamic behavior of the mechanical excitation system considering both free and forced vibrations. The influence of key parameters identified by the proposed model and their impact on machine performance is discussed. Furthermore, implications for machine design and process optimization are presented. Finally, validation of the developed model is presented through correlation of results obtained from the theoretical analysis with data from experimental tests. (C) 2015 CIRP.