The　present　paper　focuses　on　the　comparative　investigation　of　different　homogenization　methods　for　fiber　composites,　void　solids　and　rigid　inclusion　media.　The　effective　properties　of　multi-phase　media　are　calculated　by　three　methods,　i.e.　direct　average　method　of　stress　and　strain,　direct　average　method　of　strain　energy　and　two-scale　expansion　method.　A　comprehensive　comparison,　in　principle　and　numerically,　of　these　methods　is　emphasized.　It　is　obvious　that　the　two　direct　average　methods　are　identical　in　principle　and　therefore　they　give　the　same　numerical　results.　It　is　shown　that　the　two-scale　expansion　method　is　the　same　as　the　direct　average　concept　of　field　quantities　in　principle　but　is　expressed　by　different　mathematical　form　so　that　it　gives　very　close　predictions　with　that　of　direct　average　methods.