In this paper we investigate the use of ground penetrating radar (GPR) to detect corrosion-induced thinning of rebar in concrete bridge structures. We consider a simple pulse/echo amplitude-based inspection, positing that the backscattered response from a thinned rebar will be smaller than the similar response from a fully-intact rebar. Using a commercial 1600-MHz GPR system we demonstrate that, for laboratory specimens, backscattered amplitude measurements can detect a thinning loss of 50% in rebar diameter over a short length. GPR inspections on a highway bridge then identify several rebar with unexpectedly low amplitudes, possibly signaling thinning. To field a practical amplitude-based system for detecting thinned rebar, one must be able to quantify and assess the many factors that can potentially contribute to GPR signal amplitude variations. These include variability arising from the rebar itself (e.g., thinning) and from other factors (concrete properties, antenna orientation and liftoff, etc.). We report on early efforts to model the GPR instrument and the inspection process so as to assess such variability and to optimize inspections. This includes efforts to map the antenna radiation pattern, to predict how backscattered responses will vary with rebar size and location, and to assess detectability improvements via synthetic aperture focusing techniques (SAFT).