An iterative technique is employed to obtain approximate solutions to Foppl's nonlinear membrane equations. Four uniformly loaded rotationally symmetric membranes are examined: A) an annulus fixed at both edges, B) an annulus fixed at the outer edge with a rigid plug in the interior, C) an annulus fixed at the outer edge and free of tractions at the inner edge, and D) a solid circular membrane fixed at the outer edge. Numerical results are presented for each problem. The results of case D are compared with the existing exact power series solution presented by Hencky. Stresses and deflections computed by the iterative technique for case D are within 1.14% of those predicted by Hencky. a, b = e = E = F = h = Nr,Ne = q = r = Nomenclature inner and outer radii of annular membranes, respectively dilatation er + e# modulus of elasticity stress function thickness of membrane in-plane stress resultants in the radial and circumferential directions, respectively normal load intensity radial coordinate dimensionless stress resultants; Sr = Nr/(q2b2hE)ll3t u U w W