Current defect assessment procedures based on fracture mechanics usually assume flaws to be infinitely sharp. While this assumption may be appropriate for fatigue cracks, it can be an over-conservative assumption and give a large safety factor for non-sharp flaws such as porosity or weld undercut because of the loss of plastic constraint. Fracture toughness tests are performed for four types of single edge notched bend steel specimens with different degrees of plastic constraint caused by a machined-notch and a shallow notch. This paper shows the ability of the Weibull stress approach to predict brittle fracture under both high and low plastic constraint conditions. The Weibull stress approach predicts the effects accurately.