The motion of mechanically shaken filter bags has been numerically simulated with a multiple interconnected string model based on experimental investigations. Interaction between strings is modelled with two types of compatibility criteria. The model predicts the correct fundamental natural frequency of the bag and generates realistic acceleration signals at each node, needed for predicting the normal and shear stresses acting on each of many small zones of the dust cake. A complete model of dust dislodgment is established on this base in a companion paper.