Abstract: The distribution of stress and the method of same stress for uniform bolts preloads is worthy of studying during the process of tightening a flange. By analyzing the physical structure and its loading process, a mathematical model is proposed for studying the stress of bolts. The model is based on a liner-elastic model about a gasket and can predict both the scatter in bolt preloads and the ?nal clamp load distribution after the completion of joint tightening of a vessel ?ange assembly. Experimental veri?cation is provided for the validation of the mathematical model. Experimental and analytical results are presented and discussed. The model provides a good prediction for the ?nal clamp load in the join. Therefore, the novel formulation can be used to calculate and estimate the variation of bolt stress and could be used for developing tightening strategies that would achieve a more uniform clamp load in the ?ange at the initial assembly. Moreover, the model makes the process of preload without testing strain and ensure the sealing performance.