A stylized model of crop hail insurance is developed to examine the properties of the demand for such insurance. Only in the simplest case (i.e., a static model with no hail-free crop revenue uncertainty) do the results resemble those conforming to the standard theory of insurance. Allowing for crop revenue uncertainty and for dynamic updating both induce the farmer to underinsure despite an actuarially fair premium rate. The underinsurance result also emerges in a more general model • where hail insurance is purchased along with an all-risk insurance contract. In this more general model, two alternative approaches currently in use in North America are examined and their efficiency properties compared.