We present an innovative method for characterizing the distributive elastic properties in nonlinear membranes. The method hinges on an inverse elastostatic approach of stress analysis that can compute the wall stress in a deformed convex membrane structure using assumed elastic models without knowing the realistic material parameters. This approach of stress analysis enables us to obtain the wall stress data independently of the material in question. The stress and strain data collected during a finite inflation motion are used to delineate the elastic property distribution in selected regions. In this paper, we discuss the theoretical and computational underpinnings of the method and demonstrate its feasibility using numerical simulations involving a saclike structure of known material property.