The reliability of a distributed processing system (DPS) can be expressed by the analysis of distributed program reliability (DPR) and distributed system reliability (DSR). One of the good approaches to formulate these reliability performance indexes is to generate all disjoint file spanning trees (FSTs) in the DPS graph such that the DPR and DSR can be expressed by the probability that at least one of these FSTs is working. In the paper, a unified algorithm to efficiently generate disjoint FSTs by cutting different links is presented, and the DPR and DSR are computed based on a simple and consistent union operation on the probability space of the FSTs. The DPS reliability related problems are also discussed. For speeding up the reliability evaluation, nodes merged, series, and parallel reduction concepts are incorporated in the algorithm. Based on the comparison of number of subgraphs (or FSTs) generated by the proposed algorithm and by existing evaluation algorithms, it is concluded that the proposed algorithm is much more economic in terms of time and space than the existing algorithms.>