New accurate algorithms based on mathematical modeling of two parallel transmissions lines system (TPTLS) as influenced by the mutual effect to determine the fault location is discussed in this work. The distance relay measures the impedance to the fault location which is the positive-sequence. The principle of summation of the positive-, negative-, and zero-sequence voltages which equal zero is used to determine the fault location on the TPTLS. Also, the impedance of the transmission line to the fault location is determined. These algorithms are applied to single-line-to-ground (SLG) and double-line-to-ground (DLG) faults. To detect the fault location along the transmission line, its impedance as seen by the distance relay is determined to indicate if the fault is within the relay’s reach area. TPTLS under study is fed from one- and both-ends. Schematic diagrams are obtained for the impedance relays to determine the fault location with high accuracy.