Abstract: This paper is concerned with an infinite slab containing a semi-infinite crack, which is subjected to the anti-plane shear km field at infinity. The slab is made of elasto-damaged material. The analytical solution is obtained by use of conformal mapping. The shape of damage zone, damage dissipative enetgy, shear opening displacements on crack surface and some stress distribution curves are shown. The far field condition is checked. The asymptotic behavior near the tip of the crack is given.