There is by now a large literature on the economic aspects of flood control and flood relief policies. The contribution of this paper lies in its careful scrutiny of one single critical aspect of the economics of floods, the choice of land use by a single land owner. We analyze that choice using the methods of dynamic programming, and in particular, we show how that choice is dependent on the probability of floods for his piece of land. The theory we have developed here has been developed in the context of floods. In fact, this work grew out of an empirical study of flood plain damages, when we found that the underlying theory was not yet developed.! In fact, we feel that the theory is of much more general interest. It is a theory of optimal investment choice under uncertainty when that uncertainty is a result of destruction or failure of the investment at a random date. This is the case in flood plains, but it is also the appropriate basic theory for understanding investment decisions in the face of earthquakes, fires, war damage, avalanches, and other kinds of disasters. These are only the more dramatic examples of situations where replacement is required at an uncertain date.