Abstract: The warp and fill fiber strands interlacing in two mutually orthogonal directions to one another results in the fiber curvature, namely the waviness, which is the inherent characteristic of plain woven fabric composite. First, a mathematical description was developed to accurately represent the 3D architecture morphology of the unit cell for plain woven fabric composite. Next, an analytical multi-parameter model of plain woven fabric composite was established based on the classical lamination theory and iso-stress assumption. Meanwhile, the bending-extension coupling effect due to asymmetry along the thickness-direction as well as the architecture morphology of the unit cell was embedded in this model. The validation of several typical cases shows that the predicted effective elastic properties of plain woven fabric composite agree well with the numerical values of the finite element model, the results of the analytical model and the experimental data cited in the related literatures. Also, the predictions of the analytical multi-parameter model, especially the Z-direction ones, are more approaching to the experimental data than counterparts of other analytical models aforementioned. Furthermore, the influence of the structural parameters such as the waviness ratio of the fiber strand containing both the undulation direction and the cross section, the thickness of the preform consisting of the warp and fill fiber strands, the length of the curved section of the fiber strand and the spacing between the adjacent fiber strands on the elastic properties of plain woven fabric composite is elaborated. The present approach of the analytical multi-parameter model provides a reference for evaluating the mechanical properties of textile composite.