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A new material formulation to describe nonlinear hyperelastic orthotropic behaviour of composite membranes at finite strains is presented in this article. To provide numerically efficient calculations, a reduced integmtion scheme avoiding locking and hourglass instabilities is used . Restrictions concerning material parameters are discussed, and material pammeters are adapted to experimental data. Numerical calculations are used to demonstrate the potential of the appmach to inflated rubber matrix membranes applications.