In this study, the common symmetrical and unsymmetrical short circuit faults in power systems are analyzed detailed. Unlike the similar studies in the literature, metallic fault conditions for unsymmetrical faults are also given in the paper additionally. For this aim, a short circuit analysis algorithm is created for the analysis of both three phase short circuit, line-to-line short circuit with fault impedance, metallic line-to-line short circuit, double line-to-ground short circuit with fault impedance, metallic double line-to-ground short circuit, line-to-ground short circuit with fault impedance and metallic line-to-ground short circuit. The obtained algorithm is established as software in MATLAB. The algorithm is applied on a sample power test system and the results are given.