Summary: We consider a semi-infinite crack terminating at the boundary of an elastic half-space. It is assumed that the crack is subjected to a mode-I load applied in a finite region remote from the crack plane, and the boundary of the half-space and crack surfaces are free of tractions. The problem is formulated in terms of a hypersingular integral equation with respect to the relative crack-face separation defined over the region occupied by the crack. We analyze the behaviour of the solution near the corner point where the crack edge intersects the boundary, and present results which show the dependence of stress singularity exponent on the angle of inclination of crack edge.