It is known that oscillatory singularities appear in problems involving interface cracks that are assumed to have open tips. An unsatisfactory aspect of the oscillatory singularities is that they lead to overlapping of the crack faces. The interface crack in a tension field, originally treated by England among others, is thus reconsidered on the basis that the crack is not completely open and that its faces are in frictionless contact near the tips. The formulation leads to a pair of coupled singular integral equations. The singularities, no longer oscillatory, exhibit some unusual features and indicate that the spreading of the interface crack in a tension field is intimately connected with failure in shear. A new stress-intensity factor is obtained and compared to the stress-intensity factors for the completely open crack.