Peer-to-peer systems are the networks consisting of a group of nodes possible to be as wide as the Internet. These networks are required of evaluation mechanisms and distributed control and configurations, so each peer (node) will be able to communicate with other peers. P2P networks actually act as the specific transportation systems created to provide some services such as searching, large-scale storage, context sharing, and supervisioning. Changes in configuration, possibly the resultant effects of faults and failures or of the natural nodes behavior, are one of the most important features in P2P networks. Resilience to faults and failures, and also an appropriate dealing with threats and attacks, are the main requirements of today’s most communication systems and networks. Thus, since P2P networks can be individually used as an infrastructure and an alternative for many other communication networks, they have to be more reliable, accessible, and resilient to the faults, failures and attacks compared to the client/server approach. In this work on progress, we present a detailed study on the behavior of various P2P networks toward faults and failures, and focus on fault-tolerance subject. We consider two different static failure scenarios: a) a random strategy in which nodes or edges of the network will be removed with an equal probability and without any knowledge of the network’s infrastructure, b) a targeted strategy that uses some information about the nodes, and in which the nodes with the highest degree have the most priority to be attacked. By static faults, we mean a situation where the nodes or components encounter some faults before the network starts to work or through its operation, and will remain faulty to the end of the work session. Our goal is to introduce various measures to analyzing P2P networks evaluating their vulnerability rate. The presented criteria can be used for evaluating the reliability and vulnerability of P2P networks toward both random and targeted failures. There is no limit to the number and types of failures, the presented measures are able to be used for different types of failures and even a wide range of networks.