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The elastic constants are approximately determined using a multi-step linear approximation method for more accurate material nonlinear analysis of coated fabric membrane structures. The approximate determination is performed within each quadrilateral or triangular surface defined on the surfaces of the biaxial elongation property formed with the data of stress-strain curves measured by biaxial extension testings. Two types of 40 × 40 cm square flat membrane model of a PTFE coated plain-weave glass fiber fabric are analyzed applying finite element method adapting a 20-steps linear approximation method. One of the models is an inplane deformation model subjected to biaxial extension under the condition of stress ratio of 1:1. The stress-strain response in the central region of the membrane is analyzed. And the other model is a membrane deformed by the application of air pressure. The relation between the central deflection and the pressure is analyzed. The results of analysis showed excellent coincidences with experimental results.