The bolted flange structure has become a commonly used fastening connection because of its convenient installation and manufacturing cost advantages. The safety of the structure is crucially dependent on the coupling relationship of its constituent stiffness within the structure. This study proposes a multi-stiffness model of bolted flange structure based on linear elasticity theory, which incorporates elastic interaction stiffness to describe the influence of adjacent bolt. Specifically, the relationship between bolt stiffness, clamped members stiffness and interaction stiffness is derived based on the deformation coordination condition. The bolt load in the bolted flange structure is further divided into three stages. Furtherly, based on the actual loading process of bolted flange connection, a multi-stage systematic study was conducted to investigate the correlation between each stiffness and the feature parameters in the structure. By comparison with the finite element model (FEM) of the bolt-flange structure and the VDI2230 Guideline, the multi-stiffness model considering the influence of adjacent bolt was to be more accurate. Moreover, results show that when the flange thickness is small, the effect of changing the bolt spacing on the interaction stiffness is obvious.