The ultimate objective of this study has been to develop a simple model which can evaluate the lateral buckling behavior of the truss beam without using a discrete model. As a preliminary step towards fulfilling this objective, we first recognized the lateral buckling behavior of the truss beam as the out-of-plane buckling behavior of the cord member with axial force gradient. We then presented a numerical method which enables us to conveniently and systematically evaluate the elastoplastic post-buckling behavior of the cord member. However, this method does not take the elastic post-buckling behavior of the cord member into consideration, and hence it cannot be applied to the cord member with slenderness ratio larger than the critical slenderness ratio. Thus, in this paper, we extend this numerical method and present an analytical method that can accurately evaluate the elastic post-buckling behavior of the chord member with axial force gradient.