ABSTRACT: Various types of structural systems are often subjected to the risk of fatigue-induced failures. If such structural systems do not have adequate level of redundancy, local failures may initiate sequential failures toward exceedingly large damage. For risk-informed structural design and maintenance of such structural systems, it is thus essential to quantify the risk of fatigue-induced sequential failures. This paper introduces a newly developed Branch-and-Bound method employing system reliability Bounds method (termed as B3 method). Using a disjoint cut-set formulation, the B3 method identifies critical sequences of fatigue-induced failures in the decreasing order of their likelihood as it systematically updates both lower and upper bounds on the system failure probability. The updated bounds provide reasonable criteria for terminating the Branch-and-Bound search without missing critical sequences or estimating the system-level risk inaccurately. This paper presents the proposed method with numerical examples along with ongoing and future research work.