Abstract: The frqcture of materials under the action of compressive forces, directed along cracks which are parallel in plere cannot be described within the framework of the linear fracture mechanics. The criteria of fracture of the Griffith-Irvin or COC type,used in classical linear fracture mechanics, are not applicable in this problem, since these forces have no influence on stress intensity coefficients and on values of cracks opening[1,2].The problems of such a class may be described only by using new approaches.One of possible approaches is presented by the first author, which involves using linearized relations, derived from exact non-linear equations of deformable solid body mechanics[3, 4, 5]. It should be remarked here that this approach has been widely used inproblems of deformable bodies stability. As a criterion of the initiation of fracture the criterion of local instability near defects of the crack type is used. In these cases the process of loss of stability initiates the fracture process.