Abstract: The finite element mechanical analysis model was established for the prediction of elastic properties of 2D woven fabric composite. Based on the geometrical features of 2D woven fabric composite, a parameterized unit cell model was established. The anisotropic material characteristics of the fiber bundles were considered, the principal direction of the material was converted to the direction of the fiber bundles buckling, and thus the finite element model for mechanical analysis was built. The insufficiency of the plane-keep-plane assumption for boundary surfaces of unit cell was analyzed and the universal periodic boundary conditions used for 2D woven fabric composite were proposed. Therefore, more accurate engineering elastic constants of 2D woven fabric composite were obtained. Results indicate that boundary surfaces of unit cell of fabric liner present concave and convex buckling deformation under uniaxial tensile and pure shear load, namely that periodic boundary is demonstrated. Based on the fabric parameterized geometric modeling method and finite element method presented, the engineering elastic constants can be obtained accurately, and the results of the numerical simulation are consistent with that of the experiment.