A finite isotropic cracked wedge under anti plane shear deformation with a crack along  ???? = 0, 0 ≤ ???? ≤ ???? and a concentrated traction load along its radial edges is analyzed with particular consideration given to the displacement fields everywhere in the wedge. The problem is formulated using the Finite Mellin transform of the second kind, and the solution accompanied by employing the Wiener Hopf technique to obtain a closed form solution for the displacement everywhere in the wedge. It is found that at the region containing the crack, there is no continuity of the displacement fields, while continuity of the displacement fields exists in other regions of the wedge material.