The buckling delamination problem for the rectangular plate made from composite material is studied. It is supposed that the plate contains an inner rectangular crack the edge-surface of which has an initial infinitesimal imperfection. The development of this initial imperfection with an external compressive loading acting along the crack is studied in the framework of the three-dimensional geometrically nonlinear field equations of the 3D elasticity theory of anisotropic bodies. For the determination of the values of the critical force, the initial imperfection criterion is used. The corresponding boundary-value problems are solved by employing the boundary form perturbation techniques and the FEM. The numerical results on the influence of the material or geometrical parameters of the plate on the values of critical force are presented and discussed.