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. But, although a few papers have reported studies of flexural rigidity, a calculation method to estimate the flexural rigidity has remained unestablished. This paper deals with a calculation method to estimate the flexural rigidity of bolted annular flange connections subjected to an external bending moment. In the analysis, models for estimating the flexural rigidity K_b of bolts, and K_f of annular flanges are proposed, taking account of the dispersiveness of bolt disposition. Thus, a calculation method for obtaining whole flexural rigidity of bolted flange connections is proposed, using the values of K_b and K_f. For verification, experiments are performed under several conditions. Calculated results are in a fairly good agreement with experimental ones.