This paper provides a theoretical analysis of the common-pool resource dilemma in extracting nonrenewable groundwater resources when water demand is perfectly inelastic. It complements the existing theory of groundwater use, which assumes away the possibility of demand perfect inelasticity. Under perfectly inelastic water demand, the common-pool resource dilemma is by-passed if groundwater users are equally productive in water use. If they are not, a new type of inefficiency can arise due to the lack of a rationing mechanism on the basis of productivity. Our analysis suggests that groundwater management research should pay more attention to water demand elasticity and productivity heterogeneity.