Abstract This investigation concerns the accuracy with which three different J estimation schemes can predict the variation of applied Jwith applied strain for semi-elliptical surface cracks. The three estimation schemes considered were a weight function technique proposed by Bhandari, a modification of the EPRI estimation scheme proposed by Ainsworth, and Turner's Engineering- J design curve. Each of these techniques is simple enough to employ in design, the most arduous calculation required being that needed to determine the linear elastic stress intensity factor. Estimation scheme accuracy was assessed by comparing J predictions to finite-element results for three small semi-elliptical surface cracks in a moderately hardening steel loaded in either pure tension or pure bending. The results obtained indicate that, for applied strains up to three times the yield strain, both the weight function and the modified EPRI schemes under estimate applied J by between 23 and 83% depending on the applied strain level. Conversely, Turner's Engineering- ssJ design curve provides accurate or conservative (i.e. over) estimates of applied J in both tension and bending provided total crack size is less than 3% of the total cross sectional area and maximum crack depth is less than 25% of the plate thickness. Application to larger and deeper cracks loaded in tension is not recommended as the design curve does not conservatively account for net section yielding in these situations. The design curve can still be applied in bending to cracks of size up to 7.4% of the total cross sectional area. However, the degree of conservatism inherent in this application may be considered excessive in certain situations.