The authors calculate a prefracture zone, near the angular point of two different elastic-media interfaces where an interfacial crack starts, by the Wiener-Hopf method under plain strain conditions. This zone is modeled by a segment of normal displacement rupture. The dependence of the prefracture zone length and its opening at the angular point on the loading, the interface opening angle, and the medium elastic parameters is investigated. The authors study the crack starting conditions in terms of the deformation criterion.