The problem of a subsurface crack parallel and close to the surface of a semi-infinite medium was studied by dislocation modeling and finite element analysis. The loading is applied over the surface of the semi-infinite medium. For tensile loading the dislocation model gives the same result as the finite element method. For shear loading, the crack faces penetrate each other for the traction free crack surfaces. Using the ABAQUS code and the 'interface' or 'gap' elements over the crack faces, the overlap problem was avoided. It is found that one end of the crack is closed and the other is open and the Mode II stress intensity factor at the closed crack tip is larger than that at the open tip. All the stress intensity factors increase as the subsurface crack approaches the surface.