Abstract: In this paper, the improved near crack line analysis method proposed in Refs. [ 1] and [ 2] is used to investigate a center crack loaded by two pairs of antiplane point forces in a finite plate in an elastic-perfectly plastic solid. And the analytical solutions are obtained, that is, the elastic-plastic stress fields near the crack line and the law that the length of the plastic zone along the crack line is varied with an external loads and the bearing capacity of a finite plate with a center crack. The results of this paper are sufficiently precise near the crack line because the assumptions of the small scale yielding theory have not been used and no other assumptions have been taken.