Typical　pressure　vessel　materials＇　torsion　equivalent　stress-equivalent　strain　relationships　under　large　deformation　condition　are　researched　in　this　paper.　Because　the　length　and　the　diameter　of　the　specimen　may　change　under　uniaxial　tension,　it＇s　impossible　to　make　effective　measurement　and　analysis　for　the　mechanical　properties　of　the　specimen,　especially　after　the　necking.　The　form　and　cross-section　size　of　cylindrical　specimen　do　not　change　in　torsion　test,　so　that　the　large　strain＇s　constitutive　relationship　is　more　accurate　than　that　obtained　from　an　axial　tension　test.　So　that　cylindrical　specimen＇s　torsion　test　is　attempted　to　obtain　the　shear　stress-shear　strain　curves　of　typical　pressure　vessel　materials　16MnR　and　Q235.　Consider　that　the　stress　is　non-homogeneous　in　the　cross-section　of　cylindrical　specimen,　thin　wall　tube　specimen　is　also　used　in　the　torsion　test,　and　the　maximum　differences　between　cylindrical　specimen＇s　results　and　thin-wall　tube＇s　are　10%　and　13%　respectively.　Tension　true　stress-true　strain　curves,　torsion　equivalent　stress-equivalent　strain　curves　are　also　compared　in　this　paper　and　the　results　showed　that　description　of　the　torsion　constitutive　relationship　is　more　complete　than　that　of　tension.　At　last,　constitutive　equations　are　fitted　and　the　mathematical　representations　are　obtained.　©　2009　SPIE.