The general problem of nonlinear wrinkling of nonlinear membranes of revolution is considered. The theory is applicable to membranes made of any nonlinear material although only Mooney material is considered in this paper. A smooth psuedo deformed surface is introduced to give a gross representation of the true deformed surface, and a kinematic quantity called wrinkle strain is introduced to measure the wrinklyness of the surface. The wrinkly regions are determined by the usual assumption that a thin membrane cannot take any compressive stress. A stretching problem is solved as an example.

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