We consider a pre-stressed material containing an oblique crack of a length 2a situated in x1x3 plane. We supposed that the material is unbounded and the crack faces are acted by constant normal incremental stresses p. The initial applied stress ◦ is in direction of the crack. Our first aim is to determine the elastic state produced in the body using Guz’s representation theorem. Our second aim is to determine the critical values of the incremental stresses and the direction of crack propagation. To do this, we use Sih’s generalised fracture criterion for an orthotropic elastic composite. In the last part we find the critical values of the initial applied stress ◦ for which the phenomenon of resonance can appear in a pre-stressed Glass-Epoxy composite.