Abstract: The near crack line analysis method is used to investigate a crack loaded by two pairs of point shear forces in an elastic-perfectly plastic infinite plate. The analytical solutions are obtained. The solutions include: the unit normal vector of the elastic-plastic boundary near the crack line, the elastic-plastic stress fields near the crack line, the variation law of the length of the plastic zone along the crack line with external loads, and the bearing capacity. The results are sufficiently precise near the crack line since the assumption of the small scale yielding theory is not used and no other assumptions are made.