Electro-muscular disruption (EMD) devices such as TASER M26 andX26 have been used as a less-than-lethal weapon. Such EMD devicesshoot a pair of darts toward an intended target to generate anincapacitating electrical shock. In the use of the EMD device,there have been controversial questions about its safety andeffectiveness. To address these questions, we need to investigatethe distribution of the current density J inside the targetproduced by the EMD device. One approach is to develop acomputational model providing a quantitative and reliable analysisabout the distribution of J. In this paper, we set up amathematical model of a typical EMD shock, bearing in mind that weare aiming to compute the current density distribution inside thehuman body with a pair of inserted darts. The safety issue ofTASER is directly related to the magnitude of |J| at the regionof the darts where the current density J is highlyconcentrated. Hence, fine computation of J near the dart isessential. For such numerical simulations, serious computationaldifficulties are encountered in dealing with the darts having twodifferent very sharp corners, tip of needle and tip of barb. Theboundary of a small fishhook-shaped dart inside a largecomputational domain and the presence of corner singularitiesrequire a very fine mesh leading to a formidable amount ofnumerical computations. To circumvent these difficulties, wedeveloped a multiple point source method of computing J. It hasa potential to provide effective analysis and more accurateestimate of J near fishhook-shaped darts. Numerical experimentsshow that the MPSM is just fit for the study of EMD shocks.