The　bolted-flange　connection　is　one　of　the　most　popular　detachable　mechanical　joints　in　mechanical　flange　connection.　It　is　well　known　that　bolted-flange　joints　need　to　be　tightened　to　meet　the　assembly　performance　in　practical　engineering　applications.　However,　the　dispersion　of　the　pre-tightening　force　caused　by　the　elastic　interaction　between　the　bolts　has　a　serious　impact　on　the　sealing　and　safety　of　the　product,　and　therefore　the　optimization　of　bolt　preload　has　always　been　a　hot　spot　in　the　assembly　research　field.　Combining　mathematical　theory　and　experimental　data,　this　paper　proposes　an　optimization　model　for　uniformly　distributed　preload　based　on　the　Markov　theory.　The　torque　method　was　utilized　to　fasten　the　bolt-flange　joint.　The　bolt　pre-tightening　force　in　the　final　state　was　collected　and　used　as　sample　data.　A　state　transition　model　was　constructed　to　determine　the　state　transition　matrix.　Ultimately,　an　iterative　model　of　the　preload　was　deduced,　and　the　rationality　of　the　model　was　verified　through　experimentation.　The　proposed　optimization　method　of　bolt　preload　can　be　applied　to　determine　the　initial　preload　of　each　bolt.　This　method　improves　the　assembly　efficiency　and　accuracy,　which　provides　a　theoretical　approach　to　effectively　guide　the　tightening　work　of　bolted-flange　connections.　©　2022　Institute　of　Physics　Publishing.　All　rights　reserved.