We report the use of a fiber-optic distributed sensing system to monitor the shape of light-weight deployable space structures. This technique involves using optical frequency domain reflectometry to demodulate the reflected signal from multiplexed Bragg gratings that have been photoetched in the core of an optical fiber. In this work, high-resolution optical shape sensors were applied to the surface of isogrid booms and used to monitor the shape of the structure subjected to various static and dynamic loading conditions. Data from the fiber-optic sensors correlates strongly with expected results.