Ballute hypersonic aerodynamic decelerators have been considered for aerocapture since the early 1980's. Recent technology advances in fabric and polymer materials as well as analysis capabilities lend credibility to the potential of ballute aerocapture. The concept of the thin-film ballute for aerocapture shows the potential for large mass savings over propulsive orbit insertion or rigid aeroshell aerocapture. Several technology hurdles have been identified, including the effects of coupled fluid structure interaction on ballute performance and survivability. To date, no aeroelastic solutions of thin-film ballutes in an environment relevant to aerocapture have been published. In this investigation, an aeroelastic solution methodology is presented along with the analysis codes selected for each discipline. Variable-fidelity aerodynamic tools are used due to the long run times for computational fluid dynamics or direct simulation Monte Carlo analyses. The improved serial staggered method is used to couple the disciplinary analyses in a time-accurate manner, and direct node-matching is used for data transfer. In addition, an engineering approximation has been developed as an addition to modified Newtonian analysis to include the first-order effects of damping due to the fluid, providing a rapid dynamic aeroelastic analysis suitable for conceptual design. Static aeroelastic solutions of a clamped ballute on a Titan aerocapture trajectory are presented using non-linear analysis in a representative environment on a flexible structure. Grid convergence is demonstrated for both structural and aerodynamic models used in this analysis. Static deformed shape, drag and stress level are predicted at multiple points along the representative Titan aerocapture trajectory. Results are presented for verification and validation cases of the structural dynamics and simplified aerodynamics tools. Solutions match experiment and other validated codes well. Contributions of this research include the development of a tool for aeroelastic analysis of thin-film ballutes which is used to compute the first high-fidelity aeroelastic solutions of thin-film ballutes using inviscid perfect-gas aerodynamics. Additionally, an aerodynamics tool that implements an engineering estimate of hypersonic aerodynamics with a moving boundary condition is developed and used to determine the flutter point of a thin-film ballute on a Titan aerocapture trajectory.