Abrasive waterjet machining (AWJM) has been successfully used in the machining of a wide variety of engineering materials. This paper presents a new model based on the finite element analysis of the stresses generated in the workpiece material under the action of AWJ. The model is an elastic plastic Lagrangian formulation. Impact stresses were also analyzed at the cutting interface and were found to exceed the rupture strength of the workpiece material causing plastic deformation.