In this paper we describe a computational technique for simulation of the ¯uid±structure interactions of a parachute crossing the far wake of an aircraft. This technique relies on using the long-wake ¯ow data already computed, in our case, with the Multi-Domain Method (MDM) we developed earlier. The ¯uid±structure interaction computations are carried out over a domain enclosing the parachute and moving with the payload. This domain functions as one of the subdomains of the MDM designed speci®cally for the parachute ¯uid±structure interactions considered here. The boundary conditions for this subdomain are extracted from the long-wake ¯ow data, at locations corresponding to the positions of those boundaries in the subdomain over which the wake ¯ow data were computed. The Navier±Stokes equations of incompressible ¯ows, governing the ¯uid dynamics, are solved with the Deforming-Spatial-Domain/Stabilized Space±Time (DSD/SST) formulation, which can handle changes in the spatial domain occupied by the ¯uid. This formulation is coupled to the ®nite element formulation used for solving the membrane equations governing the structural mechanics of the parachute canopy and the equations governing the mechanics of the suspension lines. The numerical example included demonstrates how the technique described here, functioning as a component of the MDM, enables us to simulate the ¯uid±structure interactions of a parachute crossing an aircraft wake.