In this work, the structural integrity of the critical components of the fast breeder reactor (FBR) that are subjected thermal striping is assessed using a fracture mechanics approach based on linear elastic fracture mechanics (LEFM). The structural integrity is assessed in terms of the actual life of the component for a particular difference between the hot and cold liquid temperatures at the critical mixing velocities. A generalized procedure is attempted for the computation of fatigue life. It is demonstrated in this work that the analysis procedure adopted is computationally very efficient. Green's function method is used for transient mode I crack propagation analysis. An inherent parallelism in the method is exploited for computational efficiency. A distributed computing environment is, therefore, used to demonstrate the effectiveness of Green's function method for crack propagation analysis for the kind of problem solved in this work. A simple idealization in the form of flat plate geometry is used in a numerical example to show the computational efficiency. The method shows a good scale-up justifying the benefit of using a distributed computing environment given a large amount of input data for the thermal striping problem.