Despite the large number of abrasive waterjet machining (AWJM) models developed so far, there still has been confusion about the nature by which workpiece surfaces are eroded. The finite element method (FEM) could provide both qualitative and quantitative means in order to explain the AWJ erosion process. This paper presents an attempt to model the AWJM process using the powerful tool of the finite element method. The main objective is to develop an FE model which would enable to predict the depth of cut without any cutting experiments. The new model takes into account the pr ecise representation of the constitutive behaviour of the workpiece material under AWJ dynamic loading conditions. Interaction of the abrasive particle with the workpiece material is traced at small time increments. The model accurately predicts the depth of cut as a result of AWJ impact and the results are in good agreement with experimental results.