For better understanding of pressure vessel performance, it is necessary to clarify the effects of out-of-plane bending stress component and biaxial stresses on brittle fracture initiation. The authors carried out the burst tests of conical pressure vessel, the anticipated fracturing portion of which was subjected to biaxial stresses including an out-of-plane bending component. Every test vessel has a knuckled weld joint either convex or concave. A surface notch was provided circumferentially at the knuckled joint, in order that the tensile stress parallel to notch was not less than the perpendicular stress. Three-point bend tests and surface notched tension tests were also carried out and the results were compared with those of burst tests. The effect of parallel component of stresses on brittle fracture initiation was not observed by data analysis. So, it may be concluded that the mechanism of brittle fracture initiation established for uniaxial stress state is always applicable. As to the small scale testing, it must be noted that a sufficient acuity of notch or plastic constraint is required for the safe-side estimation of service performance.