Homogenization is an important analysis approach of composite materials with structural hierarchy and can give the prediction of macroscopic properties of the composites. There are many homogenization theories and methods. The present paper discusses applications of some homogenization approaches including both direct and mathematical homogenizations for the analysis of anisotropic composites with periodic microstructures. The macroscopic properties of the composite are predicted by the direct homogenization and the mathematical homogenisation method. The periodic boundary conditions of a representative volume element are implemented by a transformation method of the degrees of freedom. The numerical results are demonstrated for two model composites. The study shows that these two homogenization methods gave the same results for the macroscopic elastic stiffness of the composites although they are of different mathematical forms and different operation procedures.