This thesis describes the development of an accurate method of fault location in transmission lines and cables. While the presence of a high frequency transient superimposed on the 50 Hz f a u l t voltage and current waveforms must be removed for most of the transmission line protection methods, the method presented in this thesis, which draws from travelling wave principles, locates the fault position using recordings from the fault waveform independent of the frequency components present. Using the telegraph equations as a line model, voltage and current samples taken at one end of a line within the first 5 ms of fault inception were used to generate instantaneous voltage and current profiles for the rest of the transmission line. The voltage and current estimation were based on the solution of the equations of the line model by the method of characteristics. Different criteria functions, involving the computed variables were applied to determine the fault positions. The basic functions involve any one of the square of the voltage, the square of the current or the product of the two. Fault position is determined by the turning or inflexionary point in the functions. In a further development the variation of the tangent to the functions described was considered and the fault position was found to be indicated by the peak of the scatter diagram produced. This latter function finds special application for resistive faults and faults in teed networks where the turning point given by the earlier functions are not usually well defined. The algorithm has been tested both with laboratory simulations and digital computer simulated data on typical 33 kV, 132 kV and 400 kV systems. Fault location accuracies of between 0.1% to 3.3% were achieved. Following the success with laboratory tests on models, a proposal has been put forward for an on-line fault locator.