The use of entropy and resilience indices for measuring robustness of water distribution networks has been investigated. The effects on network performance, caused by the failure of one or two links, have been evaluated by means of several indices for two existing medium sized water distribution networks serving two towns in southern Italy. All the possible network configurations obtained by suppressing one or two links have been studied, excluding only the cases in which disconnection of some nodes from the remaining part of the network occurred. The hydraulic simulations, carried out with a demand-driven approach by means of the EPANET2 software, have shown that, unlike entropy, resilience may represent a useful index of network robustness with regard to link failures.