The local stress and strain in the vicinity of crack tip were calculated by means of a finite element method to examine the measuring method of crack closure points. The fatigue crack closure behavior affected the local stress σx of cracking direction much more than the local stress σy, of loading direction in the vicinity of crack tip. The diagram between the nominal stress σ representing cyclic loading and σx had some inflection points. One of them well coincided with the crack opening point. However, some undesirable inflection points due to plastic constraint or crack blunting etc. were also found on the σ-σx diagram. On the other hand, the diagram between σ and the local shear stress τ in the vicinity of crack tip was found to have clear inflection points related to the crack closure behavior. It is expected that the crack closure points can be measured easily with an adequate strain function in the vicinity of crack tip.