Based　on　the　unified　theory　for　concrete　filled　steel　tubes　(CFT)　and　the　test　results,　the　variation　of　the　concrete　confinement　effect　when　the　cross-sectional　shapes　change　from　triangle,　square,　regular　polygon　to　circular　is　investigated.　The　concrete　is　divided　into　effective　and　ineffective　confined　regions.　A　cross-sectional　efficiency　coefficient　is　introduced　to　discount　the　confinement　effect.　The　unified　circular　cross-sectional　formula　is　applied　to　calculate　the　axial　compressive　strength.　By　regression　analysis,　the　relationship　between　the　cross-sectional　interior　angle　and　the　confinement　effect　is　found.　Taking　quadrangle　sections　for　example,　the　relationship　between　the　regularity　and　the　confinement　effect　is　investigated,　and　a　calculation　method　is　provided.　By　splitting　a　special-shaped　cross-section　with　multiple　cavities　into　separate　polygons　and　considering　the　influence　of　the　shape　efficiency　and　regularity,　the　strength　of　each　cavity　CFT　is　calculated　and　summated　to　obtain　the　total　axial　compressive　strength.　The　results　show　that　in　regular　polygon　steel　tube　confined　concrete,　a　liner　relationship　is　exhibited　between　the　interior　angle　and　the　initial　tangent　line　angle　of　the　second-order　curved　boundary　between　the　effective　and　ineffective　confined　concrete　regions.　The　proposed　axial　compressive　strength　calculation　method　for　special-shaped　CFT　columns　with　multiple　cavities　can　well　reflect　the　real　confinement　features.　The　calculation　results　match　the　test　results　well　and　the　method　can　fulfil　the　engineering　design　requirements.　©　2019,　Engineering　Mechanics　Press.　All　right　reserved.