This paper presents a discontinuous smoothed particle hydrodynamics (DSPH) method to solve multidimensional discontinuous problems and the application of the method to metal penetration. The proposed DSPH method extends the original one-dimensional approximate function via Taylor series expansions and the subsequent DSPH formulations to multidimensional space. A technique proposed within the method takes any particle on the opposite side in the computational domain as a key point for discontinuous treatment, and its association with the method completes the solution for multidimensional discontinuous problems. In addition to its ability to solve multidimensional discontinuous problems, the proposed DSPH method has further capabilities of accurate physics description and efficient computation. In the first set of numerical examples, the investigation of the proposed DSPH method and its comparative study with smoothed particle hydrodynamics (SPH) method and corrective smoothed particle method have demonstrated the ability and superiority of the proposed DSPH method in solving multidimensional discontinuous problems. In the second set, the applicability of the proposed DSPH method to metal penetration has been validated by comparing the results of the proposed DSPH method to the experimental results and the behavioral analyses. Copyright © 2013 John Wiley & Sons, Ltd.