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The aim of the paper is to present the simulation of the sweeping process based on a mathematical model that includes the drag force, the lift force, the sideway force, and the gravity. At the beginning, it is presented a short history of the street sweepers, some considerations about the sweeping process and the parameters of the sweeping process. Considering the developed model, in Matlab there is done some simulation for the trajectory of a spherical pebble. The obtained results are presented in graphical shape.