Flange　connections　are　widely　used　in　various　mechanical　components.　The　most　important　purpose　of　tightening　for　flanged　bolts　is　to　achieve　designed　clamping　force　for　the　maintenance　of　overall　performance.　In　this　work,　a　multi-bolt　tightening　algorithm　is　proposed　based　on　elastic　interaction　coefficient　and　gasket　creep　relaxation.　Firstly,　dispersion　of　the　individual　bolt　clamping　forces　for　torque　control　method　is　considered　in　the　algorithm.　Relationship　between　the　nut　factors　of　the　flange　bolts　in　multi-pass　tightening　is　established　through　experiment.　Subsequently,　the　elastic　interaction　coefficient　matrix　was　updated　during　the　multi-pass　tightening　process　to　reduce　the　error.　Two　cases,　without　gasket　and　silicone　gasket,　are　considered　in　the　multi-bolt　tightening　experiment.　Without　gasket,　the　elastoplastic　deformation　at　the　initial　stage　after　tightening　will　also　cause　a　loss　of　clamping　force.　When　using　gasket,　the　clamping　force　loss　due　to　gasket　creep　relaxation　is　more　pronounced.　Through　experimental　verification,　the　proposed　multi-bolt　tightening　algorithm　are　able　to　achieve　the　target　range　of　designed　clamping　forces　and　reduce　its　dispersion.　Finally,　the　main　influencing　factors　of　the　multi-bolt　tightening　are　analyzed　to　provide　a　reference　for　the　design　of　flange　connections.