This note addresses the accuracy of the J-estimation equation for shallow-cracked single edge cracked bars, SE(B), as originally proposed by Kirk and Dodds (1993), based on 2D finite element analysis. Our study placed particular emphasis on the sensitivity of the Kirk-Dodds equation to the nature of the material, including continuously-hardening materials and those exhibiting Lüders strain. It was found that the Kirk-Dodds equation provides acceptable results except for specimen bars with very deep cracks such as those with a/W = 0.7 or greater. Accordingly, based on slip line field analysis, a modification of the original equation is suggested, which when used provides consistent results for all crack lengths.