In order to analyze the vibration of a structure whose elements are connected with bolts, it is necessary to estimate the flexural rigidity of bolted connections. Some studies have been reported on annular flange connections subjected to external bending moments. In these studies, the bolt axial force and the sealing performance are examined in detail, but their flexural rigidity is not sufficiently discussed. This paper deals with a calculation method to estimate the flexural rigidity of bolted annular flange connections subjected to external bending moments. In the analysis, a model for estimating the flexural rigidity is proposed, taking account of the dispersiveness of bolt disposition and the rigidity of flange-shell junction. That is, the annular flange is replaced with a plate and the hub with a cylindrical shell. For verification, experiments are performed. Calculated results are in fairly good agreement with experimental ones.