Abstract: Applying a geometrical method to construct the shape functions of the polygonal element, a barycentric finite element method (BFEM) for solving elastic problems was presented. The effective moduli in the transverse section of SiC/Ti and B/Al fiber composites were simulated numerically by BFEM. The computational modeling of BFEM was isotropic hexagonal representative unit cell in the transverse section of the material. The Youngs moduli, shear moduli and the bulk moduli were simulated numerically using BFEM and FEM in a wide range of volume fractions. The effective moduli in BFEM computation are in good agreement with the analytical prediction and the FEM results. In contrast to the FEM, the shapes of the elements in BFEM can be arbitrary polygons with the number of sides larger than four. So BFEM can realize the numerical simulation based on real mesostructure of the composite materials. The numerical examples demonstrate that the BFEM has higher computational efficiency and accuracy.