Abstract: The elastic-plastic analysis for a cracked plate with finite dimensions is one of the most difficult problems in fracture mechanics. In this paper, the improved near crack line field analysis method is used to analyze a centrally cracked plate with finite dimensions loaded by a pair of antiplane eccentric point forces in an elastic-perfectly plastic material. The assumptions of the small scale yielding theory are abandoned and no other assumptions are made. By matching the general solutions of the plastic fields with the reasonable elastic fields at the elastic-plastic boundary, analytical solutions of the near crack line elastic-plastic fields and the the of the plastic zone which are sufficiently precise near the crack line are obtained. The critical load for different positions of the point forces on the crack surface and for different widths of the cracked plate is evaluated.