Abstract: This paper continues the discussions to a class of method for solving problems with random boundary notches and/or cracks in references by C. Ouyang in [1] (See also [2] and [3]). Using the basic met hod given in this reference as well as some further developments. We develop here a new effective computational method for solving random deep boundary notches and/or cracks. The actual numerical computations given in this paper show that the present method is quite workable and the results obtained have enlarged the contents of "Handbook of Stress Intensity Factors" given by G. C. Sih.

Key words: option pricing, Black-Scholes model, fair premium, O-U process