In this paper, buckling delamination around interface inner cracks contained within the simply supported elastic and viscoelastic rectangular sandwich plate under biaxial loading is studied. It is assumed that the materials of the face layers are viscoelastic and the material of the core layer is pure elastic. Moreover, it is assumed that the material of the core layer is stiffer than the materials of the face layers. Within these assumptions it is supposed that between the face and core layers there are rectangular inner cracks, the locations of which are symmetric with respect to the plate geometry. The edge surfaces of the cracks have insignificant initial imperfections before the loading. The evolution of these initial imperfections with the flow of time is investigated within the scope of the three-dimensional (3D) geometrically nonlinear field equations of the theory of viscoelasticity. For determination of the values of the critical parameters (buckling force, time, and buckling mode), the initial imperfection criterion (i.e., the case where the size of the initial imperfection starts to increase and grows indefinitely) is used. Mathematical modeling of the corresponding boundary value problem is formulated within the framework of the piecewise homogeneous body model. To solve the corresponding boundary-value problems, boundary form perturbation techniques, the Laplace transform, 3D FEM modeling and the Schapery method are used. The numerical results related to the influence of the materials or geometrical parameters of the plate on the critical parameters and critical time are presented and analyzed.