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Nowadays, the design of textile membrane structures is based on the strong simplification of a linear elastic material behavior with different elasticity moduli in warp- and weft-direction. In this contribution it is shown by comparing with experimental data that this assumption is not satisfactory for specific loading situations. A material model formulation in the framework of the continuum mechanics provides the ability of a more accurate description of the nonlinear anisotropic material behavior. Therefore, a hyperelastic model neglecting visco-elasto-plastic properties is proposed for the steady-state situation taking into account the nonlinearity of the material response. In addition to that, a finite element formulation based on a shell theory is provided which enables simulations making use of the proposed material model. A numerical example shows the possibilities of such simulations and the potential for the construction of textile membrane structures by exploiting an optimal arrangement of the warp- and weft-directions.