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The near crack line analysis method has been used in the present paper. The classical small scale yielding conditions have been completely abandoned in the analvses and one inappropriate matching condition used to be used at the elasricplastic boundary has been corrected. The reasonable solution of the plastic stresses near the crack line region has been established. BJJ matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary, the ptasric stresses. the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crack line region have been obtainedfor a mode I crack under uniaxial tension, as well as a mode I crack under biaxial tension, which shows that for both conditions the plastic stress components uV and cr.#, the length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same white the plastic stress fl., is different.

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