The singular stress field at a crack tip can be presented by the Williams series,where the constant term is named T-stress.The constant term and non-singular terms,which are called general T-stress here,play a significant role in determining the stress and strain fields around a crack tip which in turn can affect the calculation of stress intensity factor(SIF) of the crack.Herein,a new method which combines the singularity eigen-analysis with the boundary element method was proposed to determine the general T-stress in the crack tip.Then the effect of the general T-stress on the calculation of the stress intensity factor of a crack was studied.The numerical results show that the stress intensity factors taking account into the general T-stress are more proximate to the experiment results.