An automatic self-cleaning filter is a semi continuous machine operated for the removal of particles from a fluid. Technically, a distributor driven by a hydraulic motor rotates at regular intervals to feed the slurry to the inlet chambers of N segmented elements horizontally stacked over the distributor and back-flushes the last chamber. In this work a practical computationally-affordable model has been developed to describe the distribution of flow rate in the different sectors of a disc-type element and to demonstrate the effect of parameters, such as backflushing time or pollution concentration, accounting for particle clogging and periodic operation conditions for perfect and imperfect efficiency of the cleaning by back-flushing. The key results are the prediction of the time of clogging, as well as a numerical tool to optimize critical back-flushing time and pollution concentration.