This paper demonstrates that the material removal processes employed during abrasive water jet (AWJ) cutting show evidence of Self Organised Criticality (S.O.C.). This means that the overall erosion process consists of a large number of events which are identical except for their size. The relative frequency of these self-similar events is related to their magnitude by a power law, for example an erosion event of relative magnitude 100 may be accompanied by 10 exp 3 of magnitude 10 and 10 exp 8 of magnitude 1. As the mechanism of step formation and localised erosion has been establish in earlier work (4, 5, 6), it is reasonable to postulate that the numerous self similar erosion events are of this type. It is demonstrated that for ductile material (such as metals) and brittle material (such as glass) the abrasive water jet cutting mechanism obeys the laws of self organized criticality