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