Axisymmetric boundary value problems in nonlinear elastic membrane theory are studied, with prescribed tensile stresses or radial displacements at the edge(s). The membrane of revolution is subjected to a load parallel to the axis or normal to the deformed surface. Analytical and numerical methods are presented to determine the range of boundary data for which the solutions are tensile and stable in the sense that the principal stresses are nonnegative everywhere in the membrane.

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