The supersonic parachute inflation dynamics (PID) of the Advanced Supersonic Parachute Research (ASPIRE) SR03 parachute system, represented by a detailed computational model, are numerically simulated using a high-fidelity framework for fluid–structure interaction (FSI). Numerical results, in the form of representative quantities of interest, are validated against data from the ASPIRE SR03 flight test. The validation is performed on a predefined array of numerical simulations in order to investigate the robustness of these results and establish their sensitivities to identified critical modeling assumptions, including the resolution of the computational fluid dynamics mesh, the choice of the constitutive law for material modeling, and the choice of which physics to include. These sensitivities are evaluated with attention to their development and computational costs and to their associated uncertainties. The ultimate goal of the reported work is to pave the way for establishing best practices for the numerical simulation of supersonic PID and to advance the potential role of computational FSI in the design and evaluation processes of aerodynamic decelerator systems in general.