The buckling delamination around the band cracks contained with the simply supported all edge-surface rectangular sandwich thick plate is investigated. It is assumed that the sandwich plate is composed of two face layers and a core layer. Face and core layers are made of different materials and it is assumed that there are two same cracks at the interfaces between the layers. Material of each layer is isotropic and homogeneous. For the solution procedure it is supposed that the surfaces of the cracks have insignificant initial imperfections. The development of this initial imperfection with an external compressive loading acting along the cracks is studied in the framework of the three dimensional geometrically nonlinear field equations of the elasticity theory and the piece-wise homogeneous body model. For the determination of the values of the critical force the initial imperfection criterion i.e. the case where the imperfection starts to increase and grows indefinitely, is used. The corresponding boundary value problems are solved by employing the boundary form perturbation techniques and the three dimensional FEM. The numerical results on the critical force are presented and analyzed. The influences of the material and geometrical parameters on these critical values are discussed.