Although there have been several numerical models used by different authors to model microstructural behaviour of a woven fabric-reinforced composite ply, they all suffer from geometric simplifications that may affect their validity or at least accuracy of results. This paper presents an enhanced model of a representative volume element RVE of this kind of composite with the plain-weave fabric pattern. Many important simplifications are overcome while the mathematical description remains simple. A dedicated FE mesh generator allows to reproduce all geometric details in the computational model. Computational examples of homogenization of orthotropic elastic constants illustrate application of the model.