By the very nature of their origin through shrinkage effects, residual stress states can be expected to be triaxial in large structures. Investigations have been carried out into the effects of residual stresses on constraint and on fracture behaviour by means of finite element analyses and local fracture criteria. Three dimensional finite element analyses including the effects of large elastic plastic deformation have been conducted on centre cracked plates subjected to various residual stress fields and transverse externally applied loads. It has been found that tensile longitudinal residual stresses parallel to the crack flank increase constraint while compressive stresses in this direction have the opposite effect. A bi–axial residual stress state can increase constraint effectively even in the case of the longitudinal stress component parallel to the crack flank being compressive. Results of full field 3D finite element analyses for stresses at the crack tip have been discussed in relation to the 2D T–stress analysis. It has been shown that the concept of the T–stress is not readily applicable in the presence of residual stresses unless primary and secondary stresses are treated separately. Cleavage fracture toughness levels of the less constrained centre–cracked wide plates may be reduced to below the toughness levels of the highly constrained bend specimen because of residual stress effects. The effect of residual stresses on the initiation of ductile fracture has also been demonstrated.