A three-dimensional buckling delamination problem for a rectangular sandwich plate made from elastic and viscoelastic materials is studied. It is supposed that the plate contains interface embedded rectangular cracks and that the edge-surfaces of these cracks have initial infinitesimal imperfections. The evolution of these initial imperfections with an external bi-axial compressed force (for the case where the materials of the layers of the plate are elastic) or with duration of time (for the case where the materials of the layers of the plate are viscoelastic) is investigated. The corresponding boundary value problem is formulated within the framework of the piecewise homogeneous body model with the use of three-dimensional geometrically nonlinear field equations of the theory of viscoelastic bodies. This problem is solved by employing boundary form perturbation techniques, Laplace transform and FEM. According to the initial imperfection criterion, the values of the critical parameters are determined. Numerical results on the critical force and critical time are presented and discussed. In particular, it is established that the values of the critical forces obtained for the buckling delamination around the rectangular embedded interface cracks are significantly greater than those obtained for the corresponding edge and band cracks.