A 3D buckling delamination problem for a simply supported rectangular orthotropic composite thick plate containing a rectangular crack and subjected to an axial compressive force is studied. In the initial state, crack faces have an infinitesimal imperfection. The development of this imperfection caused by an external compressive loading along the crack is investigated within the framework of the 3D geometrically nonlinear elasticity theory of anisotropic bodies. The corresponding boundary-value problems are solved numerically by the 3D FEM. The influence of material and geometrical parameters of the plate on its critical buckling force is evaluated and discussed.