This article presents a calculation of the elastic moduli of a monatomic fluid of rigid spheres. Although calculations for monatomic systems with a continuous and differentiable interatomic potential indicate that the elastic moduli become infinite as the potential becomes infinitely repulsive, we find that the hardsphere moduli are nonsingular, and well defined. This result leads one to suspect that a fluid with a highly repulsive, but continuous and differentiable, interatomic potential may not always be even qualitatively represented by a fluid consisting of perfectly rigid spheres. Our method of attack consists of finding the general form of the stress tensor for a hard-sphere system, asserting the assumptions of local equilibrium, and expanding the stress tensor in terms of the strains using the techniques developed by Green.
