In this paper, we focus on fluid–structure interaction (FSI) modeling of ringsail parachutes, where the geometric complexity created by the “rings” and “sails” used in the construction of the parachute canopy poses a significant computational challenge. It is expected that NASA will be using a cluster of three ringsail parachutes, referred to as the “mains”, during the terminal descent of the Orion space vehicle. Our FSI modeling of ringsail parachutes is based on the stabilized space–time FSI (SSTFSI) technique and the interface projection techniques that address the computational challenges posed by the geometric complexities of the fluid–structure interface. Two of these interface projection techniques are the FSI Geometric Smoothing Technique and the Homogenized Modeling of Geometric Porosity. We describe the details of how we use these two supplementary techniques in FSI modeling of ringsail parachutes. In the simulations we report here, we consider a single main parachute, carrying one third of the total weight of the space vehicle. We present results from FSI modeling of offloading, which includes as a special case dropping the heat shield, and drifting under the influence of side winds.