The near crack line analysis method is used to investigate a center crack loaded by two pairs of point tensile forces in an infinite plate in an elastic-perfectly plastic solid, and the analytical solutions are obtained in this paper. These solutions include: the elastic-plastic stress field near the crack line, 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 infinite 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.