This paper successfully proposes a new method of searching for the best linearization point (β-point) in the Advanced First-Order-Second-Moment Method. The method has been applied to reliability analysis of a structural element subjected to a bending moment and axial force, and the failure probabilities evaluated by the various failure criteria are compared. It is concluded that a linearized failure criterion gives a conservative estimate of reliability of the structural element, and that it is also valid for the slenderness ratio of 40∼60.