Most reliability-based analyses focus on the reliability of the individual components of a structure. There are many advantages to examining the components in combination as an entire structural system. This paper illustrates an algorithm used in the computer program RELSYS (RELiability of SYStems) which computes the system reliability of any structure which can be modeled as a series-parallel combination of its components. A first-order method is used to initially compute the reliability of each individual component. The system reliability is computed by successively reducing the series and parallel systems until the system has been simplified to a single equivalent component. Equivalent alpha vectors are used to account for the correlation between failure modes during the system reduction process.