Periods of banking distress are often followed by sizable and long-lasting contractions in bank credit. They may be explained by a declined demand by financially impaired borrowers (the conventional financial accelerator) or by lower supply by capital-constrained banks, a "credit crunch". This paper develops a bank model to study credit crunches and their real effects. In this model, banks maintain a precautionary level of capital that serves as a smoothing mechanism to avert disruptions in the supply of credit when hit by small shocks. However, for larger shocks, highly persistent credit crunches may arise even when the impulse is a one time, non-serially correlated event. From a policy perspective, the model justifies the use of public funds to recapitalize banks following a significant deterioration in their capital position.