A model of dust collection and removal from mechanically shaken filters has been established closely based on previous experimental investigations. This numerical model includes three principle stages: (a) the basic particle filtration equation is used to describe the process of dust collection at each of many small zones on the filter bag; (b) the motion of the filter bag during shaking is numerically simulated with a multiple interconnected string model that predicts the normal and shear forces on the interface between dust cake and bag; and (c) the concept of fatigue crack growth coming from fracture mechanics is introduced to model the dislodgment of the dust cake. The crack growth is calculated through the normal and shear forces imposed on the dust. Many aspects of the behaviour of this fairly complex dynamic system have been successfully reproduced.