The ability to accurately estimate the extent to which the failure of a bank disrupts the financial system is very valuable for regulators of the financial system. One important part of the financial system is the interbank payment system. This paper develops a robust measure, SinkRank, that accurately predicts the magnitude of disruption caused by the failure of a bank in a payment system and identifies banks most affected by the failure. SinkRank is based on absorbing Markov chains, which are well-suited to model liquidity dynamics in payment systems. Because actual bank failures are rare and the data is not generally publicly available, the authors test the metric by simulating payment networks and inducing failures in them. They test SinkRank on several types of payment networks, including Barabási-Albert types of scale-free networks modeled on the Fedwire system, and find that the failing bank’s SinkRank is highly correlated with the resulting disruption in the system overall; moreover, the SinkRank algorithm can identify which individual banks would be most disrupted by a given failure.