Starshade concepts must be stowed within rocket fairings for launch and then deployed in space. The in-plane deployment accuracy must be on the order of hundreds of micrometers for sufficient starlight suppression to enable the detection and study of Earth-like exoplanets around nearby Sun-like stars. We describe tests conducted to demonstrate deployment repeatability of two key structural subsystems of the “furled” starshade architecture—the petal and the inner disk. Together, the petals and the inner disk create the in-plane shape of a starshade. Test articles to represent the petal and inner disk subsystems were constructed at relevant scales for a 26-m-diameter starshade. These test articles were subjected to stowage-and-deployment cycles and their shapes were measured. The measured performance—tens of parts per million of petal strain after deployment, and hundreds of micrometers of inner disk deployment accuracy—was found to be within required allocations.