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This paper discusses the asymptotic analysis of two- and three-dimensional stress concentration regions, prior to and after the development of a crack. Previously obtained asymptotic expressions for two-dimensional notches with a finite root radius pO are reviewed, and existing stress field solutions for extreme values of pO are recast in asymptotic form. Expected results for cracks growing in geometrically similar notches are discussed. It is then shown that the asymptotic character of the stresses for uncracked three-dimensional stress concentration regions is virtually identical to that of the planar case. Finally, the paper outlines techniques for finding the asymptotic modes for three-dimensional cracked stress concentration regions, which are likely to be otherwise analytically intractable.