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Due to the integration of distributed generations and the realization of smart grids, most radial distribution systems would become weakly meshed in the near future. Thus, this paper proposes an efficient and accurate short-circuit fault-analysis method for unbalanced weakly meshed distribution systems. Two proposed matrices developed from the radial and weakly meshed characteristics of distribution systems are used to analyze the variations of bus voltages, bus-current injections, and branch currents under fault conditions. Accordingly, some efficient and effective formulas are derived in this paper to analyze the effects of different fault types on the weakly meshed distribution systems. Traditionally, unsymmetrical faults are analyzed by the symmetrical-component-based method; however, this method is usually time-consuming due to the building process of impedance matrix. The proposed method can provide novel viewpoints in calculating fault effects; and therefore, can achieve the advantages of high speed and improved accuracy with lower memory requirements. Test results demonstrate the efficiency and accuracy of the proposed method.