The near crack line analysis method is used to investigate an eccentric crack loaded by shear forces in a finite plate,and the analytical solution are obtained.The solutions include: the unit normal vector of the elastic-plastic boundary near the crack line,the elastic-plastic stress fields near crack line,law that the length of the plastic zone along the crack line is varied with an external loads,the maximum lengths of the plastic zone,the bearing capacity of a finite plate with an eccentric crack loaded by shear forces.The results are sufficiently precise near the crack line because the assumptions of the small scale yielding theory have not been made and no other assumption have been taken.