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.