The use of the detached eddy simulation (DES) approach is investigated for the study of rigid supersonic disk-gap-band parachute aerodynamics related to the Mars Science Laboratory mission. The flow around the suspended spacecraft capsule and the resulting unsteady wake are resolved with the CFD method. It is found that the time-varying momentum deficit in the capsule wake interacts with the bow shock on the canopy, producing a highly unsteady flow. The simulations show that the canopy over-pressurizes, expels the excess gas, resulting in collapse of the bow shock and subsequent over pressurization. This alternating over- and under-pressurization is strongly correlated with the bow shock motion and the axial drag on the parachute. We feel that this mechanism is responsible for the sometimes violent dynamics of supersonic disk-gap-band parachutes and the partial skirt collapse that these parachutes experience. The computational and numerical method requirements for performing these unsteady simulations are discussed, as well as grid generation strategies.