A new method is presented for parametrically generating optimal shapes and stresses of a membrane structure supported by a frame. The problem considered here is a so called trade-off design problem where the weighted sum of the deviations of the initial stress and the shape from the desired distribution is to be minimized. The membrane is discretized by using the finite element method, and optimal shapes are expanded with respect to a parameter defining the shape of the boundary frame. An approximate method is presented without exact calculation of the Hessian of the stresses with respect to the nodal coordinates. The explicit developability conditions derived by the authors are used to guarantee the curved surface to be reduced to a set of plane cutting patterns after removing the pretensioning force. In the examples, trade-off designs are found for an HP-type membrane structure and the efficiency of the proposed method is discussed. (C) 2000 Elsevier Science S.A. All rights reserved.