This study presents a new fault location algorithm for multiple-circuit shared tower transmission lines with different voltages utilising synchronised measurements. The formulation of the proposed algorithm is based on overhead transmission lines theory and Taylor series expansion of distributed-parameter line model. The untransposition of the lines and the mutual coupling between the parallel lines are considered to achieve precise fault location. Kirchhoff's current law and fault location equation are used to identify the faulty section and obtain the location of all normal shunt faults and inter-circuit faults. The power system is simulated with DIgSILENT Power Factory software and all calculations are performed by MATLAB. Numerous fault cases are conducted to demonstrate the efficacy of the proposed algorithm considering different values of fault resistances, different fault locations and all fault types. In addition, the effects of synchrophasors errors, measurement errors and the soil resistivity variations are investigated. The results of simulation prove the efficacy of the proposed algorithm for all fault cases.