Modeling and studying the impact of single angular particles are very helpful in understanding the fundamental mechanisms of erosive wear. However, the majority of previous studies focused on well-defined symmetrical particles, which are not well representative of the abrasive particles. Hence, this study develops a mesh-free model based on the smoothed particle hydrodynamics (SPH) method to simulate impact(s) of single arbitrary-shaped particles on ductile material. A novel procedure is proposed to model the particle as a polygonal rigid body through measuring the corner vertices. The ductile material properties are modeled by using the  equation of state and the Johnson–Cook model. Simulations are carried out by varying the initial input conditions and by using different types of angular particles. Common erosion mechanisms such as cutting, machining, ploughing, prying-off are successfully reproduced by the model. The predicted crater is compared with available experimental data, and good agreement has been achieved. The proposed SPH model and out present study could be useful in the study of erosive wear on the surface of metal devices that carries granular substances.