Recently, trust establishment is recognized as an important approach to defend distributed networks, such as mobile ad hoc networks and sensor networks, against malicious attacks. Trust establishment mechanisms can stimulate collaboration among distributed computing and communication entities, facilitate the detection of untrustworthy entities, and assist decision-making in various protocols. In the current literature, the methods proposed for trust establishment are always evaluated through simulation, but theoretical analysis is extremely rare. In this paper, we present a suite of approaches to analyze trust establishment process. These analysis approaches are used to provide in-depth understanding of trust establishment process and quantitative comparison among trust establishment methods. The proposed analysis methods are validated through simulations.