The viscoelastic plastic model of vibration movement of ore particles along the vibration organ was described. The model includes viscoelastic and elastic plastic blocks. The first one describes elastic deformations of the system and measures energy losses using a damper. The second block describes plastic (residual) deformations. The differential equations of model motion at different stages of ore particle movement were analyzed. Two mathematical models were presented using second and third order differential equations. Recommendations to simplify the model at various stages of movement were suggested. Research models of various levels of complexity were developed. At the stage of particle movement along the vibration organ, it is not advisable to simplify the viscoelastic plastic model in the direction normal to the organ. It is advisable to simplify the model in the direction of the working surface of the vibration organ at the stage of non-slip interaction by eliminating the elastic-plastic block. When the particle is sliding along the vibration organ and flying, the model should be simplified to a rigid body. These simplifications facilitate the task of developing algorithms and software for the vibration process under study.