A method for estimating the decrease in crack-initiation toughness, from a reference plane-strain value, due to positive straining along the crack front of a circumferential flaw in a reactor pressure vessel, is presented in this study. This method relates crack initiation under generalized plane-strain conditions with material failure at points within a distance of a few crack-tip-opening displacements ahead of a crack front, and involves the formulation of a micro-mechanical crack-initiation model. While this study is intended to address concerns regarding the effects of positive out-of-plane straining on ductile crack initiation, the approach adopted in this work can be extended in a straightforward fashion to examine conditions of macroscopic cleavage crack initiation. Provided single-parameter dominance of near-tip fields exists in the flawed structure, results from this study could be used to examine the appropriateness of applying plane-strain fracture toughness to the evaluation of circumferential flaws, in particular to those in ring-forged vessels that have no longitudinal welds. In addition, results from this study could also be applied toward the analysis of the effects of thermal streaming on the fracture resistance of circumferentially oriented flaws in a pressure vessel.