Safety analysis can be labour intensive and error prone for system designers. Moreover, even a relatively minor change to a system's design can necessitate a complete reworking of the system safety analysis. This paper proposes the use of Behavior Trees and model checking to automate Cut Set Analysis (CSA) : that is, the identification of combinations of component failures that can lead to hazardous system failures. We demonstrate an automated incremental approach to CSA, in which models are extended incrementally and previous results incorporated in such a way as to significantly reduce the time and effort required for the new analysis. The approach is demonstrated on a case study concerning the hydraulics systems for the Airbus A320 aircraft.