This paper introduces two alternative formulations of a fault location algorithm, based on two-point measurements, which is appropriate for unbalanced medium voltage overhead distribution systems of radial configuration with or without distributed generation. The first alternative is solely based on synchronized three-phase voltage signals taken from the two measurement points. The algorithm applies fundamental bus-impedance-matrix-based fault analysis theory and calculates voltage drops to derive a fault location equation set for each fault type. The standard bus impedance matrix theory is also the basis for the second alternative. By combining the expressions correlating unsynchronized voltage and currents measurements from the two points with the elements of a modified bus impedance matrix, the need for synchronization angle is eliminated. Then, a fault location equation set is formed to obtain the fault distance and resistance. A multiple solutions elimination methodology is also proposed which is applicable for both alternative fault location algorithms addressed in this paper Extensive simulation studies demonstrate a good performance for the proposed fault location algorithms under numerous short-circuit conditions with varying pre-fault system loading conditions, fault resistances and measurement errors.