Taking inflatable structures of stratospheric airships as the main study object, the minimum differential pressure and the stress of inflatable structures were computed according to its design theory and a finite element model of inflatable structure for stratospheric airship was established. On the basis of the model verification, nonlinear finite element method was applied to simulate inflatable structural performance so as to obtain the distribution and change laws of the deformations and stresses of inflatable structure with the variations of pressure load and gondola load. The effects of structural reinforcement devices on the stress and deformation of inflatable structure also were evaluated. The simulation results can serve as reference for the structural design of the stratospheric airship.