Many　engineering　materials　and　structures,　such　as　cellular　structures,　sandwich　core　structures　and　laminated　plates　with　holes,　can　be　modeled　by　an　inclusion　problem　with　anisotropic　matrix.　The　paper　studies　the　effective　properties　and　the　microscopic　deformation　of　anisotropic　plates　with　periodic　holes　by　using　direct　and　mathematical　homogenization.　The　effective　stiffnesses　are　calculated　by　different　homogenization　methods　and　the　microscopic　deformation　of　a　RVE　is　modeled　by　the　finite　element　method　for　the　plate　with　arbitrarily　shaped　holes.　All　of　the　effective　stiffness　coefficients,　especially　stretching-shear　coupling　coefficients　are　evaluated.　(C)　2004　Elsevier　Ltd.　All　rights　reserved.