The investigation of scattering of waves by cracks in an elastic medium and by thin scatterers in an acoustic medium, via analytical and experimental methods, seems to be of continuing importance to nondestructive evaluation. On the analytical side, formulation and numerical solution of crack scattering problems using boundary integral equations is popular and effective because of the very nature of a crack, but this approach still suffers some shortcomings of an analytical nature. That is, the governing equations in their primitive form involve a hypersingular kernel function, and the usual process of regularization to lower the kernel singularity usually introduces undesirable features in the analysis accompanied by computational difficulty.