This paper shows that bank runs can be modeled as an equilibrium phenomenon. We demonstrate that some aspects of the intuitive “story” that bank runs start with fears of insolvency of banks can be rigorously modeled. If individuals observe long “lines” at the bank, they correctly infer that there is a possibility that the bank is about to fail and precipitate a bank run. However, bank runs occur even when no one has any adverse information. Extra market constraints such as suspension of convertibility can prevent bank runs and result in superior allocations.