This monograph presents a new strain based probabilistic fracture mechanics approach for large plastic deformation analysis of through wall cracked pipes subject to an external bending load in combination with internal pressure (bi-axial loading). Strain-based fracture mechanics equations, including the effects of bi-axial loading have been presented to study the behavior of through wall cracked pipes.High Dimensional Model Representation concepts are explored to approximate the original implicit limit state/performance function in terms of crack length, internal pressure and material hardening. Subsequently the failure probability is obtained by performing Monte Carlo simulation.In addition, studies on off-center through wall cracked pipes have been carried out, to observe the effect of off-center angle on fracture response and failure probability.The study well emphasized the capacity of the off-centered cracked pipes in comparison with the symmetrically centered cracked pipe.Finally, an alternate procedure for J-estimation is proposed using reference strain formulations for assessing the fracture response of the through wall cracked pipes subjected to bi-axial loading.