Abstract: The improved near crack line analysis method was used to investigate an eccentric cracked plate loaded by two pairs of anti-plane point forces at the crack surface in an elastic-perfectly plastic solid. The analytical solutions of the elastic-plastic stress fields and displacements near the crack line have been found without the assumptions of the small scale yielding. The law that the length of the plastic zone along the crack line is varied with an external loads and the bearing capacity of an eccentric cracked plate are obtained.