Does economic activity move away from areas that are at high risk of recurring shocks? We examine this question in the context of floods, which displaced more than 650 million people worldwide in the last 35 years. We study large urban floods using spatially detailed inundation maps and night lights data spanning the globe’s cities. We find that low-elevation urban areas are flooded more frequently, and yet they concentrate more economic activity per square kilometer. When cities are flooded, low-elevation areas recover as rapidly as those higher up. With the exception of recently populated urban areas, we find little permanent movement of economic activity in response to floods. (JEL O18, Q54, R11, R58)