A gamma-ray scattering densitometer was developed for the nonintrusive measurement of the local void fraction in complex geometries. The densitometer system consisted of a shielded 137Cs photon source, a NaI photon detector, and a collimator system that defined the scattering volume within which the photons were scattered. An analytical model for the scattering events was developed. This model took the form of an integral equation, which expressed the measured counting rate in terms of the geometric configuration, local density, and the nuclear properties of the scattering volume. An interactive-graphics-based numerical procedure for inversion of the integral equation was developed. Results of two-phase flow measurements in a concentric annulus are given.