The current limits of supersonic parachute technology may constrain the ability to safely land future robotic assets on the surface of Mars. This constraint has led to a renewed interest in supersonic inflatable aerodynamic decelerator (IAD) technology, which offers performance advantages over the DGB parachute. Two supersonic IAD designs of interest include the isotensoid and tension cone, named for their respective formative structural theories. Although these concepts have been the subject of various tests and analyses in the 1960s, 1970s, and 2000s, significant work remains to advance supersonic IADs to a technology readiness level that will enable their use on future flight missions. In particular, a review of the literature revealed a deficiency in adequate aerodynamic and aeroelastic data for these two IAD configurations at transonic and subsonic speeds. The first portion of this research amended this deficiency by testing flexible IAD articles at relevant transonic and subsonic conditions. The data obtained from these tests showed that the tension cone has superior drag performance with respect to the isotensoid, but that the isotensoid may demonstrate more favorable aeroelastic qualities than the tension cone. Additionally, despite the best efforts in test article design, there remains ambiguity regarding the accuracy of the observed subscale behavior for flight scale IADs. Due to the expense and complexity of large-scale testing, computational fluid-structure interaction (FSI) analyses will play an increasingly significant role in qualifying flight scale IADs for mission readiness. The second portion of this research involved the verification and validation of finite element analysis (FEA) and computational fluid dynamic (CFD) codes for use within an FSI framework. These verification and validation exercises lend credence to subsequent coupled FSI analyses involving more complex geometries and models. The third portion of this research used this FSI framework to predict the static aeroelastic response of a tension cone IAD in supersonic flow. Computational models were constructed to mimic the wind tunnel test articles and flow conditions. Converged FSI responses computed for the tension cone agreed reasonably well with wind tunnel data when orthotropic material models were used and indicated that current material models may require unrealistic input parameters in order to recover realistic deformations. These FSI analyses are among the first results published that present an extensive comparison between FSI computational models and wind tunnel data for a supersonic IAD.