An accurate and reliable material model for plain weave coated fabrics used in the construction of Tensioned Fabric Structures (TFS) is developed in this paper. The paper begins with an account of the material response of these fabrics, furnishing an understanding of the key elements that a successful material model should encompass. The paper also contains a review of existing models, which has highlighted the need for an accurate, reliable and fully calibrated material model. The proposed material model consists of a series of nonlinear elastic elements, frictional elements and rigid links to model the yarns, and an isotropic plate to model the coating. The high degree of accuracy and reliability attained is demonstrated through comparison against experimental results. This is attributed to faithfully capturing the major deformation mechanisms that prevail in TFS, which include crimp interchange, yarn extension and crushing, friction, coating extensions and fabric shear. The success of this work paves the way for accurate and reliable analysis of TFS, providing better control and assessment of stress states encountered in the field.