Abstract：Based on the stress—strain relationship and the deformation compatibility conditions，the basic equation of the circular membranes stretched the outer edge radially is established．The analytic solution is given through in— troducing the non—dimensional parameters to simplify the basic equations．The formulae of the stress distribution are obtained by theoretical derivation，and the conclusion shows that the radial stress and the circumferential stress is equal，and the stress values are the same at different locations，and the stress values al"e proportioned to the va1． He of the radial displacement．The correctness of the analytic solution is certificated by the way of finite element simulation．