As an emerging space return technology, the inflatable reentry vehicle provides a new technical solution for deep space exploration, recovery of target spacecraft, and freight transport of space products. Aimed at the serious structural failure of inflatable reentry vehicle induced by the aeroelastic effect in transonic and supersonic flows, a fluid-solid coupling approach considering the effect of the inflation gas is established. The proposed model comprehensively considers the nonlinear factors of flexible inflatable film and the feedback of structural deformation on flow field. Based on this model, the static and dynamic aeroelastic problems under transonic and supersonic conditions are carefully studied. The obtained results reveal that the depressed deformations of flexible skin hinder the flow near surface and aggravate the degree of stagnation and heat dissipation, causing the surface temperature and pressure field significantly growing compared to the case of undeformed situation. Under action of the dynamic aeroelasticity, the violent low-frequency vibration induced by the turbulent wake occurs on the vehicle, which is more serious at the transonic stage condition (about Ma 0.8) or asymmetric incoming flow. The performed research indicates that the effects of the static and dynamic aeroelasticity should be fully taken into account in the design process of inflatable reentry vehicles, giving insightful guidance for engineering practice.