In this paper the general plane problem for a semi-infinite strip fixed at its short end, containing a crack perpendicular to its voundaries is considered. The strip is under the effect of a stamp. By extending the crack to the surfaces, one can reduce the problem to that of c cantilever beam or plate. Integral transform technique is used to provide an exact formulation of this problem, in terms of a system of four singular integral equations one of them being second kind. Stress singularities at the corners of the fixed-end, at the crack tips and at the end points of the contact region undermeath the stamp are obtained from the singular integral equations which are then solved numerically.