A theoretical basis is investigated for the extrapolation techniques of determining crack tip stress intensity factors. The extrapolation technique proposed by Chan et al. is based on the first three terms of the asymptotic expansion of crack tip stress or displacement (i.e., containing γ-1/2, γ0 and γ1/2 for stress, containing γ1/2, γ and γ3/2 for displacement), and the second term equalling zero is the absolute requirement of straight line extrapolation. From this viewpoint, the conditions for which the extrapolation technique can be available are presented for the problems of Mode I only, Mode II only and the mixed Mode condition. Improved extrapolation procedures are presented in the case when the crack face is subjected to arbitrary tractions. These theoretical results are confirmed by use of the boundary element method (BEM) analysis for center cracked plate problems of Mode I only and mixed Mode conditions.