Fault tree analysis is an efficient technique for predicting the reliability of complex systems. One of the major problems in such analyses has been the extensive computations, which are required, to predict the probability of occurrence of the events under consideration; and consequently, the reliability of a whole system. The repetition of some events in the fault tree causes additional difficulties and is one of the principal sources of exhaustive computational effort. This thesis presents a method for the analysis of fault trees which reduces the complexity caused by the presence of repeated events, thus minimizing computing time and storage requirements. The new method is amenable for hand calculations, as well as computer implementation, thus allowing very large fault trees to be handled in a fraction of the time required by conventional methods. A step by step procedure to obtain the minimal cut sets of a fault tree, by the new method, is presented and applied to some sample fault trees. Compared to the conventional method, the new method yielded a reduction of computing time from about 15% to 8 0% and a reduction in working space requirements of about 6 5% for a typical example.