The problem of local buckling delamination around interface edge cracks in a sandwich PZT/Metal/PZT rectangular thick plate is studied within the scope of the 3D linearized buckling instability theory. Crack faces have an insignificant initial imperfection, and the plate is compressed by uniformly distributed normal forces acting on two opposite ends of the plate. The evolution of the initial imperfection is investigated, and the critical buckling forces for the plate are found. A mathematical modeling of the problem considered is performed using the 3D exact geometrically nonlinear electroelasticity theory within the framework of a piecewise homogeneous body model. The corresponding boundary-value problems are solved numerically by employing a 3D finiteelement method. Numerical results for the critical forces and the effect problem parameters on these forces are presented and discussed.