In this paper we consider the effect of the free surface on the stress distribution of an elliptic crack aligned parallel to the free boundary and at a depth h below it. The title problem is posed as a dual integral equation in Cartesian coordinate system. By suitable transformation the dual integral equation is first reduced to an infinite system of dual integral equation in cylindrical coordinates. Then they are further reduced by a recently developed technique to an infinite system of Fredholm integral equation of the second kind. When the boundary is at a large distance away from the crack, the system of integral equation is solved by perturbation technique as powers of δ = a/h, a being the length of semi major axes and h the depth of the crack below the boundary. The analytical expressions for the three stress-intensity factors at the crack edges for normal loading are given upto order δ5. Effect of the boundary on the stress-intensity factor is illustrated graphically. © 1992.