A nonlinear anisotropic hyperelastic constitutive model is developed for plain weave fabrics by considering biaxial tensile coupling. The strain energy function is decomposed into two parts to represent tensile energy, including the biaxial tensile coupling effect from fiber elongation and shearing energy from relative rotation between warp and weft yarns. A simple and efficient material parameter identification method is proposed. The model is exemplified on a balanced plain weave glass fabric. Experimental data from the literature are used to identify material parameters in the constitutive model. Model validation is implemented by comparing numerical results with various experimental data, including biaxial tension tests under different stretch ratios and the picture frame shearing test. The developed constitutive model is applied to numerical simulation of a double-dome stamping of the plain weave fabric. The influences of binder force and initial fiber yarn orientation on forming are investigated. Numerical results demonstrated that the biaxial tensile coupling effect could not be neglected in forming simulation. The developed constitutive model is suitable to characterize the nonlinear behavior of plain weave fabrics under large deformation.