Abstract: The hypothesis of small yielding conditions is used in the stress analysis near crack in traditional mechanics,while the near crack line analysis method gives out this hypothesis.So the near crack line analysis method is used to investigate a crack loaded by a pair of point shear forces in an finite plate with an eccentric crack in an elastic-plastic solids.The analytical solution of the stress near crack line and precise analysis of the elastic-plastic boundary are obtained.The research gives out the hypothesis of small yielding conditions.On the basis of the near crack line analysis method，the elastic-plastic stress fields near crack line is analyzed，and the law that the length of the plastic zone along the crack line varied with an external loads is established by the matching condition of the elastic-plastic fields on the boundary.

Key words: near crack line analysis method, typeⅡcrack, elastic-plastic analysis, an finite plate, an eccentric crack