<p>This dissertation explores the stability of beams, plates and membranes due to subsonic aerodynamic flows or solar radiation forces. Beams, plates and membranes are simple structures that may act as building blocks for more complex systems. In this dissertation we explore the stability of these simple structures so that one can predict instabilities in more complex structures. The theoretical models include both linear and nonlinear energy based models for the structural dynamics of the featureless rectangular structures. The structural models are coupled to a vortex lattice model for subsonic fluid flows or an optical reflection model for solar radiation forces. Combinations of these theoretical models are used to analyze the dynamics and stability of aeroelastic and solarelastic systems. The dissertation contains aeroelastic analysis of a cantilevered beam and a plate / membrane system with multiple boundary conditions. The dissertation includes analysis of the transition from flag-like to wing-like flutter for a cantilevered beam and experiments to quantify the post flutter fluid and structure response of the flapping flag. For the plate / membrane analysis, we show that the boundary conditions in the flow direction determine the type of instability for the system while the complete set of boundary conditions is required to accurately predict the flutter velocity and frequency. The dissertation also contains analysis of solarelastic stability of membranes for solar sail applications. For a fully restrained membrane we show that a flutter instability is possible, however the post flutter response amplitude is small. The dissertation also includes analysis of a membrane hanging in gravity. This systems is an analog to a spinning solar sail and is used to validate the structural dynamics of thin membranes on earth. A linear beam structural model is able to accurately capture the natural frequencies and mode shapes. Finally, the dissertation explores the stability of a spinning membrane. The analysis shows that a nonlinear model is needed to produce a conservative estimate of the stability boundary.</p> / Dissertation