The buckling delamination problem for a rectangular composite plate with a rectangular inner crack subjected to biaxial compressive forces is considered. It is assumed that the plate considered is simply supported at all its lateral sides, to which uniformly distributed compressive forces are applied. It is also supposed that the surfaces of crack faces have initial infinitesimal imperfections before loading of the plate. The evolution of these imperfections under the action of the biaxial compressive forces is studied within the scope of the threedimensional geometrically nonlinear field equations of the theory of elasticity for anisotropic bodies. For determining the critical buckling delamination force and the buckling delamination mode of the plate considered, an initial imperfection criterion is used. For solution of the corresponding boundary-value problems, the boundary-form perturbation technique and the 3D FEM are employed. Numerical results illustrating the influence of the materials and geometrical parameters of the plate on the critical force are presented and discussed.