Understanding the exact nature of erosion of workpiece materials by abrasive waterjet machining (AWJM) is still confused, although it is important for successful modeling of this promising process. This paper presents a first attempt to model the AWJM process using the powerful tool of the finite element method (FEM) in order to explain the abrasive particle-workpiece interaction. Also the model predicts the behaviour of the process. 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 precise representation of the constitutive behaviour of the workpiece material under AWJ dynamic loading conditions which was ignored in previous AWJM models in which the flow stress was represented by a constant value. Additionally, deformations, stresses and strains occurring in the workpiece material in the vicinity of the cutting interface as a result of the erosion impact by AWJ, could be obtained. In the present model, forces acting on the abrasive particle need not be initially determined, as in previous AWJM studies, as they are automatically calculated at each time step. The results show that the finite element method is a useful tool in predicting abrasive-material interaction and AWJ depth of cut.