Abstract: This paper continues the discussions to a class of method for solving problems with random boundary notches and/or cracks in refs. [1] and [2]. Using the method developed in [1],[2] with important modifications about inclusion of singularities in the formulation, we arrive at a very effective computational process for problems with random boundary orucks. Actual computations for boundary cracks with or without applied tractions in their surfaces. Show that the present method is quite workable for the problems considered within proper range of characteristic parameters. The results obtained here extend the contents of "Handbook of Stress Intensity Factors" given by G. C. Sih.

Key words: Taylor series, convergence and summability of series, homotopy analysis method, perturbation