The strains parallel to the crack front for a circumferential flaw in a pressure vessel are tensile, as opposed to zero (plane strain) or compressive (plane stress). It is reasonable to expect that this tensile strain condition may influence the constraint at the tip of the circumferential flaw. A series of axisymmetric nonlinear finite element analyses have been performed to investigate the nature of the crack tip stress fields and constraint for the limiting case of a continuous inner circumferential flaw, with an emphasis on comparing these fields and constraint levels to those in a plane strain configuration having the same geometric configuration and subjected to axial loading only. The focus of these investigations is on constraint implications for cleavage initiation in the lower transition region at realistic pressure vessel load levels; in addition, the results provide some insight into constraint implications for ductile fracture under higher load levels. Constraint is quantified using: (a) the extent of the yielded zone, (b) a hydrostatic stress triaxiality factor, (c) the elastic second-order stress term (T-stress) and the near tip elastic-plastic second-order stress term (Q-stress—O'Dowd and Shih, 1991 [24]). The analysis results suggest that the cleavage-relevant constraint measures for the circumferential flaw under combined internal pressure, crack face, and axial loading are comparable in magnitude to those in the corresponding plane strain condition at low J values; at higher J values, however, the circumferential flaw under combined loading exhibits significantly lower constraint levels than those in the plane strain reference condition. The reduction in constraint at higher J values in the circumferential flaw case is found to be caused principally by the negative in-plane stress biaxiality induced by the internal vessel pressure loading rather than by the out-of-plane tensile strain influence.